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Tsubasa and Arisa from Arisa. Arisa is loved by everyone at her school, has good grades and is the Class Representative. Tsubasa is nicknamed "the Demon Princess" and is constantly getting into fights and has lousy grades. As it turns out, Arisa is very much a Broken Ace.
Baka to Test to Shoukanjuu: The Nice Guy Hideyoshi and the Jerkass Yuuko. Further differences include that Hideyoshi is not smart enough to qualify past Class F (the bottom of the barrel), while Yuuko is in Class A (the best), and Hideyoshi is a beautiful singer but Yuuko is completely tone-deaf.
Digimon Frontier: Kouji and Koichi. Kouji is arrogant and kind of a jerk at first, working by himself because he thinks the others will only drag him down. As time goes on, he shows a much kinder side. His Digimon forms are wolf-based and his element is light. Meanwhile, his twin is similar in appearance but far more soft-spoken and willing to be in the group once he's de-brainwashed. And, his Digimon forms are lion-based and his element is darkness (Dark Is Not Evil.)
D.N.Angel: Riku and Risa even come out and say that their personalities are completely different. Risa is very girly and rather shallow (most of the time), while Riku is tomboy-ish and more down to earth.
Durarara!!: Mairu and Kururi Orihara actually invoked this. They actually flipped a coin to decide which girl got which trait. Strangely enough, their roles (Mairu as the Genki Girl and Kururi as The Quiet One) switch when they're on the internet. Even weirder is the fact that they don't consider themselves separate people.
Eyeshield 21: The Kongo twins Unsui and Agon. Unsui has a shaved head like a monk (it's sort of a theme at their school) is intensely hard working, diligent, cautious, a very good athlete and basically a decent guy. But Agon (with a distinctive dreadlock hairstyle) is the series' Jerk Ass, a Jerk Jock to the extreme (including the womanizing, which apparently started in middle school) who gets away with being a sociopathic thug, slacker and general all-around asshole because he is a talent seen only once in a hundred years.
It emphasized by the fact that 'A' and 'Un' represent "beginning and end" aka birth and death.
Fushigi Yuugi gives us easygoing, kind, polite Amiboshi contrasted to Hot-BloodedJerkass Suboshi. Heck, even their weapons are different: Amiboshi has a flute which he can use for Mind Control on his opponents (for good or evil purposes), and Suboshi prefers to just smash through everything with a Killer Yo Yo. Even their clothes reflect just how opposite they are: Amiboshi wears a blue tunic, and Suboshi wears an orange one. (At least in the series; in promo artwork, they are very frequently dressed exactly alike.)
Takuma and Kazuma from Gakuen Babysitters. The former is perpetually cheerful, and the latter is perpetually teary-eyed.
Glass Fleet's Vetti and Cleo exemplify this trope. Though, their personalities are passed off as them having been raised separately, with the younger one subjected to mental and sexual abuse, giving him his screwed up personality.
Fuka and Fumika Narutaki of Mahou Sensei Negima!. The former's the trouble-making class pankster while the latter's constantly worried about how the former's pranks will get them in trouble as she gets dragged along.
Gundam Seed has Kira and Cagalli. The former is quiet, polite, and kind to a fault. The latter is brash, flippant, and has quite a temper. Also one's a boy and one's a girl.
Monster: Anna and Johan Liebert. Anna's a nice, sweet girl who practices aikido and delivers pizza as a part-time job. Johan is the title character.
Yuma and Yuna Kashiwagi from Pani Poni Dash!. Yuma is an extreme extrovert, Yuna is an extreme introvert. Yuma goes so far as to actively sabotage Yuna's attempts at being more accepted just to keep eyes on her.
Ranma ˝: Towards the end of the manga, there is Pink and Link, identical twin girls from a village of herbalists that neighbours Shampoo's village of "Chinese Amazons" and who practice different branches of an unnamed "Martial Arts Herbalism", a fighting style that revolves around plants and herbalistic concoctions. Pink, who is usually smiling, is a wicked and vicious girl who loves to poison people. Link, who is usually frowning, is a kind and gentle girl who considers it her duty to heal those her sister hurts. Despite these opposite natures, they care for each other deeply and are capable of uniting with singular purpose when given motive... which means that, in their actual appearance in Nerima, they function more like Single-Minded Twins.
Suiseiseki and Souseiseki from Rozen Maiden are very much this, both including a Tomboy and Girly Girl relationship, but with several more differing characteristic traits. Where Souseiseki is stoic, Suiseiseki is emotional. Souseiseki is serious and collected, while Suiseiseki is mischievous. Souseiseki believes it is the duty for every doll to participate in the Alice Game regardless of personal attachments, while Suiseiseki strictly opposes the Alice Game due to fear of losing her sisters.
Spirited Away: The identical twin sisters Yubaba and Zeniba. Yubaba is selfish and materialistic; Zeniba, while vengeful at first, turns out to be kindly and humble.
Tenshi Ni Narumon: Noelle (the light) and Silky (the darkness) as described by Mikael. Mikael and Raphael might also count
Vash is also all about how other people feel and love and peace, and Knives doesn't even do empathy for his twin with whom he has an effing psychic link.
Vash acts like a fool whenever he can and Knives is all superiority and icy control except when his temper gets away from him. They do have a bit in common still, when you get past the good and evil divide. For instance, scary if you get them mad. Stubborn as hell. Charisma. Way of speaking, when serious, is even a little similar. Pretty good, when you consider they've been separated over a hundred times as long as they were together.
When they were kids in the anime, one was unusually mature and one was goofy. No prizes for which. In the manga, they were much more similar, but Vash was more outgoing and Knives was more sensitive.
Anime Knives goes off and cuts his own hair while Vash is getting his first haircut from Rem; when Vash finds him he says "if we stay the same, we won't have any individuality," even though they're pretty distinct already and even have slightly different coloring, because Viewers Are Morons.
Saint Seiya has the twin brothers Saga (thoughtful, wise, just until his Superpowered Evil Side kicks in) and Kanon (selfish, scheming, arrogant until he has a Heel-Face Turn.) For major irony, Saga is the Gemini Saint, with Kanon inheriting his position once Saga dies. In Saint Seiya Omega we have Gemini Paradox who has a crazy split personality and good, loving, kind Gemini Integra. Same thing happens. Paradox is beaten by Ryuuho, and Integra picks up the Gemini Cloth afterwards during the Pallas War.
Rua and Ruka (Leo and Luna, respectively, in the dub) from Yu-Gi-Oh! 5Ds. Rua is a rowdy, cocky duelist who overestimates himself. Ruka is quiet, introverted and is usually the one to notify Rua when he goes too far.
The original series' Yugi and Yami Yugi can be counted as this if you consider them twins (of the split personality/alternate guy living in your head kind), with a dash of Sibling Yin-Yang.
Hamel and Sizer from Violinist of Hameln. Hamel is loud, obnoxious and tends to spaz out while his sister Sizer is calm, sensible and serious. He's arrogant and loves to boast while she's a bit shy and doesn't like a lot of attention. Them being opposites is also emphasized by the fact Hamel is half demon while Sizer is half angel, and she starts as a villain while Hamel is the hero.
Jezebel and Dinah in Blacksad: Dinah is a black bear (= dark brown) with a white patch on her chest, Jezebel a polar bear (= white) with a dark patch on her chest. Otherwise, they share face structure, and body and hair type. Personality-wise, Dinah is softer and Jezebel harder, although both have it in them to do what they need, if it's for righteous revenge.
Ember and Suntop in Elfquest. She is a fiesty, red-headed partially wolf-blooded mortal Wolfrider who is destined to become the next Chief of the Wolfriders. He is the complacant, magical, blonde, immortal grandson of the mystic leader of the Sun Village and the apprentice of the equally mystic Mother of Memory. Word of God is that they actualy chose these different destinies while in the womb.
In X-Men Noir, Thomas and Robert Halloway are, respectively, a know-it-all afflicted with Chronic Hero Syndrome and a crude, violent sadist. It's probably important to note that they were adopted by different families after their father died.
Star Wars: Luke is a blonde, blue-eyed, calm, mild-mannered, naive, mystical, religious Jedi Knight. Leia is a brunette, brown-eyed, quick-tempered, sharp-tongued, worldly-wise, shrewd, practical politician.
The Star Wars Expanded Universe shows Luke having trouble teaching Leia to be a Jedi. What worked for him (he got a lot of Jedi qualities) won't work for her. Hot temper is not something a Jedi knight ought to have. Especially since she's pregnant with Han's baby while trying to learn.
The Parent Trap: In the 1998 remake, the twin girls, Annie James and Hallie Parker (Lindsay Lohan), are completely different. Annie is calm, reserved, and rather uptight while Hallie is relaxed, loud, outgoing, and a Big Eater. (Compare Annie with Cody and Hallie with Zack of The Suite Life.)
Susan and Sharon in the original, to a lesser extent.
Markus and William Corvinus, from Underworld Evolution, were twin brothers who respectively became the first vampire and first werewolf. One is scheming and pompous, the other is near-mindless and savage. Unusual in that we never learn if they'd been genetically identical or not, as William is already locked permanently in his wolf-man form at the time the film is set, but they probably were.
Charlie and Donald Kaufman in Adaptation have completely opposite approaches to screenwriting and to life.
In Double Trouble, David is an honest cop with slobby habits, and his brother Peter is an unrepentant cat burglar with a taste for culture.
The whole concept of Film/Twins is that Arnold Schwarzenegger and Danny Devito play genetically-engineered twins, with Arnold being the product of attempting to make the perfect man and Devito being all the "genetic garbage" they were weeding out of Arnold.
Polgara and her twin Beldaran in the Belgariad series. The former is dark-haired, has a grim disposition, and grew up to be an immortal sorceress. The latter was blonde, had a sunny disposition, and married young to become the queen of an island kingdom and bear the royal line which would deliver the child of prophecy, before dying young of pneumonia. As Polgara's biography explains, the two were originally much more similar, but their mother tampered with them in the womb to prepare them for their destinies.
Occurs in Gordon R. Dickson's Childe Cycle series of novels and short stories, in the characters of Ian and Kensie Graeme. Both are Dorsai (Proud Warrior Race Guys). Ian is the epitome of the Warrior - seemingly aloof and intimidating by his sheer presence. Kensie is his polar opposite - warm, caring, social - everything that Ian is not. In the stories it's implied that together the two make up one individual.
Lampshaded in The Legendsong Saga. Glynn and Ember are twins who are both physical and personality opposites. Their only physical similarity is the same colour eyes (yellow); personality contrasts include Ember’s musical talents and Glynn being tone-deaf.
Shaun and Shem from Finnegan's Wake probably count, but it's hard to figure out which is which, due to the book changing their names constantly. All you need to know is one is boring and dull, and the other is really creative and artistic.
Specifically, Shaun is dull and conformist but successful in society, while Shem is a slovenly outcast but also an artistic genius.
Owen and Porter from First Person Plural by Andrew Beierle. Owen is a book-reading drama nerd. Porter is a cheerleader-dating football player. Owen is gay, and Porter is straight. They are also conjoined twins sharing one body with two heads. This is incredibly awkward considering that Porter married a homophobic woman.
Nicky and Alex in the Full House book series grew up to be different, one tough, one shy, although in one episode of the show their father was concerned that their personalities would turn out the other way around.
The Eiran twins Eamonn and Grainne from Kushiel's Dart by Jacqueline Carey.
In the original Story Lottie and Luise by Erich Kästner (aka "Das doppelte Lottchen"), the titular twins had extremely different personalities, which made their place change all the more hilarious, and later difficult. Luise was a cheerful, bratty tomboy while Lottie was a sensible, serious, prim and proper girl who behaved almost like a grown-up. Most film versions omit this aspect.
Eve and Alexandra in Master of the Game are a Cain and Abel crossover version — Alexandra is sweet, honest, and innocent, with no ambitions towards running Kruger-Brent, Ltd. Eve is consumed by ambition and the desire to be the center of everyone's attention, and starting from the age of five she's determined to kill and/or ruin Alexandra, who's in the way. (Incidentally, author Sidney Sheldon co-created the much gentler Trope Namer years before.)
Abby and her twin sister Anna of The Baby-Sitters Club. Anna is musical, bookish, and introspective; Abby is athletic, noisy, and enjoys babysitting. About the only things they have in common are that they both have scoliosis and poor eyesight.
Dawn and Eve of Piers Anthony's Xanth are literally as different as day and night, from the fact that Dawn is red haired and green eyed, and is like the morning, while Eve is black haired and eyed and is like the night.
Both the books and TV version of Sweet Valley High, with the Wakefield twins Jessica and Elizabeth.
In Pierce's Circle of Magic universe, Nia the shy, retiring one (with woodworking magic) and Jory the hyperactive, overeager one (with cooking magic).
Tatterhood and her unnamed twin sister from the Norwegian fairytale are a perfect example of this: Tatterhood is an ugly, but spirited Badass Princess who rides on a goat and singlehandedly beats up hordes of trolls and witches, while her sister is a beautiful, but helpless Damsel in Distress. Despite this, the twins are inseparable and get along famously.
The flesh-mind and aggression of Esau the hunter versus the faith and docility of Jacob the homemaker in The Bible. In fact one book of children's Bible stories even had the chapter title "Twins Who Were Different."
Amoret and Belphoebe in The Faerie Queene: The former was adopted by Venus, the Goddess of Love and Beauty, and became a Proper Lady. The latter was adopted by Diana, the Goddess of Maidenhood and the Hunt, and became an Action Girl.
Emmeline and Adeline March from The Thirteenth Tale, who are totally passive and excessively violent respectively.
The twins in Flowers in the Attic Cory is quiet, polite and gentle. Carrie is loud, adamant and forceful.
Web Serial NovelCorrespondence From The Goddess has Lydia Devin, the main character, a snarky aimless twentysomething who slowly gains divinity-level powers over the course of the story, and Elana Devin, her twin sister, who is perfect as perfect can be but doesn't seem to have any powers at all.
Live Action TV
Madison and Vida Rocca from Power Rangers Mystic Force. Madison is calm and thoughtful, V is on a permanent sugar high and goes rushing into things with a mad grin.
Two of a Kind and So Little Time, both with Mary-Kate and Ashley Olsen. The twins played this up in most of their TV-movies as well. Ashley nearly always played the responsible one with Mary-Kate as the wild one. This finally got reversed in Winning London where Mary-Kate was bookworm and straight-A-student Chloe while Ashley was relaxed Lad Ette Riley.
Friends gives us twin sisters Phoebe and Ursula, the first being a (mostly) light-hearted and cheery Cloudcuckoolander, with the second being mean-spirited, thoughtless, and, in Phoebe's words, a "real high-powered, driven career-type" (she's a waitress).
The '80s sitcom Double Trouble. Identical twins Jean and Liz Sagal (younger sisters of Katey Sagal of Married... with Children) play identical twins Kate and Allison. Allison is serious and bookish; Kate is happy-go-lucky.
Scoundrels, Cal and Logan West, an incompetent burglar/criminal, and an intelligent defense lawyer, respectively. The characters are so different, you can barely tell they're played by the same actor.
This is a remake of a New Zealand show, Outrageous Fortune, with Van and Jethro West in the same roles (also played by the same actor).
The good and evil brothers in The Wanderer. Dispite both being played by Bryan Brown it isn't at 'all' difficult to tell Adam from Zachary, the evil cackle gives it away every time.
iCarly: Sam and Melanie Puckett. The former is almost permanently grouchy, borderline sociopathic, and sarcastic, while the latter is upbeat, outgoing, and perky. Notably, Carly says she can't believe that they're sisters. They agree.
Lee and Leah, the Separated at Birth twins from the British teen show The Gemini Factor, a rebellious boy and a teacher's pet girl, with a sprinkling of Twin Telepathy. They also tended to wear black and white, respectively.
Katie and Emily Fitch from Skins. In the beginning Katie is portrayed as the shallow, popular, boy-obsessed Alpha Bitch, and Emily as the sweet, socially-awkward Shrinking Violet (and closet lesbian) who does everything her bossy sister says, until she comes out of the closet and begins dating her girlfriend Naomi. But when both girls suffer a series of severe personal setbacks they handle it very differently, with Katie gaining a lot more depth and maturity, having to hold the family together virtually on her own, and Emily becoming more and more angry and destructive.
Cathy and Patty Lane from The Patty Duke Show. "But they're cousins, Identical cousins all the way. One pair of matching bookends, Different as night and day."
SCTV parodied the show, running promos for "Identical Bellhops", "Identical Cheese Hostesses" and "Identical OPEC Oil Ministers", all shoehorning their titles into the familiar theme song.
Patricia and Piper Williamson from House of Anubis. Patricia is the bold, Tomboyish, defiant and rude one; Piper is highly talented in piano, very sweet and polite, and much less inclined to make big moves out of fear of failure than her Determinator sister is. It's pretty obvious when you compare their crushes- Patricia likes Jerk with a Heart of Gold Eddie, while Piper likes the Nice GuyClass Clown Alfie.
In the Scamp (Son ofLady and the Tramp) comics (Specifically the newspaper continuity), Scamp and his siblings are two sets of these. Twin Sisters Fluffy and Ruffy are dignified and tomboyish, respectively, while non-identical brothers Scamp and Scooter are adventurous and timid, respectively.
In The Bible, we have Jacob and Esau. Esau is the older one, and he displays a Carpet of Virility and is a skilled hunter. Jacob is younger, and isn't so hairy and prefers to use his brains over brawn. Which enables him to receive Esau's birthright. They were at odds with one another before they were even born!
The Wood Elves of Warhammer Fantasy have Naestra and Arahan, polar opposite personalities in identical bodies produced when Naestrahan was split into two women due to an unknown event deep in the woods of Athel Loren. They ride a dragon.
High Elf Heroes Tyrion and Teclis are identical twins with radically opposing personalities and skills. Tyrion is proud, fair, noble, athletic and well-spoken, while Teclis is dark, feeble, scholarly, caustic-tongued and bitter. The one is the greatest warrior and commander of his race but has no talent for sorcery, the other is a poor fighter but the most powerful living wizard in this age of the world.
Warhammer's elves really seem to be prone to this trope, as another example can be found in the 5th edition Tears of Isha campaign pack, which focuses on the war between Calaidan and Kaldor, twin scions of the High Elf house Coraith, one of whom defects to Naggaroth and becomes an evil Dark Elf while the other inherits the family estates and continues their proud High Elven traditions.
Ravenloft's Laurie and Gennifer Weathermay-Foxgrove are identical twin monster-hunters and proteges of Rudolph van Richten. Laurie is an exuberant tomboy, fencer and pistoleer who dresses like a man, while Gennifer is a demure, sober-minded wizard with closets full of conservative dresses. Also, Gennifer may be an unwitting lycanthrope.
A number of the gods in pre-Fourth Edition Forgotten Realms were opposed siblings, though they usually looked noticeably different—Shar and Selune (the moon and the dark), Tymora and Beshaba (good and bad luck), Vhaeraun and Eilistraee (drow thieves, often male, and redeemed drow, often female).
Final Fantasy IV: Palom and Porom. Palom is the bouncy, mischievous user of black magic, and Porom is the serious-minded user of white magic.
The GetBackers game Jagan Fuuin The Mikado twins: Daisuke is very compassionate and sweet and easily befriends the main cast, whereas his identical twin Kyosuke is cold, emotionless, rarely speaks, and seems robotic. It's eventually revealed that the twins are the same person, namely Kyosuke, who, due to fear of their immense spiritual power, were split into two entities, the "body" and "soul". Daisuke was the soul, and once they were merged back into Kyosuke, he acted much like his "brother" did.
Street Fighter: Hyperactive Yun and brooding Yang of the Lee Brothers.
Tokimeki Memorial 2 has the twin sisters Miho and Maho Shirayuki. Miho is a sweet, daydreaming girl who believes in fairies, and loves fortune-telling and plushies, and dreams of becoming a scenario writer of stories for children; Maho is a playful, blunt and mischevious street-wise girl, who enjoys fashion and window-shopping, and dreams of becoming a model.
The WarCraft universe. Malfurion and Illidan Stormrage, the night elf twin brothers. The former leads his people to druidism as an alternative to the dangerous magic that brought the Burning Legion to Azeroth. The latter insists on tapping both that magic and the power of the demons themselves, is imprisoned for centuries and eventually becomes an Evil Overlord.
The Davis twins are described as "different as night and day" within the game, yet they actually have identical personalities and aspirations. The only real difference between them is their appearances and what they like to talk about. Similarly, the Pleasant twins in Pleasantview are supposedly very different, but have very similar personalities.
Fire Emblem Elibe introduces another pair in Lugh and Ray. Lugh is a cheerful mage (specializes in elemental magic), while Ray is a cold and calculating shaman (specializes in dark magic).
The Bruiser Brothers in Super Punch Out. Rick Bruiser is outgoing and hotblooded, while Nick Bruiser is quiet and cold.
The Neptunia series has the extrovert Ram and the shy Rom. These twins are also a huge source of irritation for their big sister, Blanc.
A double battle in Pokémon X and Y features a duo of sisters, one is a happy, friendly, Fairy Tale Girl, and the other is a shy, introverted, Hex Maniac.
Greg and Sidney Kasal from Trauma Center. Sidney is serious and straight-laced, while Greg is far more relaxed.
Ace Attorney: Dahlia and Iris from the third game. Dahlia is a ruthless sociopath who has been using her cute and innocent image to get away with murder, literally, for years and Iris is sweet, gentle, and compassionate, and honestly fell for the lead character while posing as her sister because she needed him for a master plan but didn't want to be bothered with actually seducing him.
CLANNAD: Kyou and Ryou. Long-haired tsundere and short-haired easily-embarrassed sweetheart.
Tsukihime: Kohaku and Hisui. One is carefree, energetic and always smiling, while the other is silent with little expression.
Also odd, when you consider that they switched places from when they were children. Hisui was originally carefree and cheerful, while Kohaku was shy and untalkative. Then they got older and things got worse for them (specially Kohaku, so Hisui buried her emotions to keep Kohaku stable while Kohaku hid her very darkened True Self behind a facade of happiness.
Ember and Daystar in the ElfQuest visual novels. Ember is active, bold and like her name in looks and attitude. Brother Daystar is mystical and calm, and blond with pale skin.
Little Busters! has Haruka and Kanata, who form an All Work vs. All Play duo. In reality, though, these roles were mainly either in response to or outright enforced by their abusive extended family and in the end when they are able to move on from their past and accept one another as friends their personalities become a lot less extreme. Not entirely, though.
It's Walky!: Fraternal twins Beef and Walky. Justified as Beef was actually switched at birth with Walky's real twin Sal as part of Mrs. Walkerton's Separated at Birth gambit, Sal and Walky later, after the truth was uncovered, and used to set up some Not So Different moments between the two of them.
Sal and Walky again in Dumbing of Age despite not being raised apart this time around.
LnM: L is energetic and childish, M is laid back and precocious.
Molly and her clone/twin Galatea in The Inexplicable Adventures of Bob! were raised separately. Both are brilliant, naive, and devoted to Bob, Jean, and each other. But while Molly is upbeat, friendly, and gentle, Galatea is paranoid and megalomaniacal.
The Order of the Stick has Elan and Nale, who look the same except for a goatee on Nale, but their personalities are complete opposite. Elan is good, naive and Genre Savvy, while Nale is an evil and scheming. It turns out that Elan got his goodness from his mother and his genre savvyness from his father, while Nale got his evilness from his father and his affinity for schemes from his mother. Their opposite is also indicated by their names.
Doki is much different than her twin sister Toki. Both dress somewhat alike but wear different colors: black or purple for Toki, reflecting her enigmatic but secretly kindhearted personality, and pink and white for Doki, reflecting her kind, gentle, and angelic personality.
American Dragon Jake Long: Oracle twins Kara and Sara. It's played around a bit as it is gothic Kara who foresees good events in the future while blonde and preppy Sara forsees the bad events.
Their powers are why their personalities are so different. Kara is always depressed and gloomy because everything good about to happen gets spoiled for her, and Sara is always so happy because any time the horrible things she sees aren't happening is absolutely fantastic in comparison.
Dragon Tales: Zak and Wheezie, who are even very different colors!
ElfQuest: Suntop and Ember actually brought the Media Watchdogs down on them when their creators tried to get an Animated Adaptation going. Turns out Saturday Morning Cartoons is not the time to reverse genders roles and have a spunky little girl and a mild, intuitive little boy. Or, for that matter, twins with different skin colors.
America's Next Top Model: Amanda and Michelle Babin, who were contestants on Cycle 7. Michelle is tomboyish and more outgoing, whereas Amanda is more feminine and introverted. Michelle also came out of the closet during the course of the show, just to add another night and day difference to the mix.
Tokio Hotel: Bill and Tom Kaulitz are identical twins, but dress and wear their hair differently, just to name one difference, to the point that some people don't believe they're identical. One of the more notable differences is Bill's focus on "true love" while (until recently) Tom was only looking for love of the one-night variety.
The public perception of the Kray twins has traditionally had Ronnie, the younger twin, as pure Ax-Crazy psychopath, and Reggie as quieter and more Affably Evil, even acting as something of a Morality Chain to his brother. There's not necessarily much evidence of this, but that just makes the fact that people want it to be the case an example of this trope in action.
Happens to twins in Real Life, as twins growing up together try to develop different personalities to distinguish themselves from their sibling. However this is usually subverted in identical twins - twins that came from the same zygote, not from two different zygotes in the womb - as they are practically genetically identical copies of each other and will share many similarities in personality and preferences even if they act differently. National Geographic has done an article on it.