In Toy Story 3, it turns out Lots-o'-Huggin' Bear used to be just like Woody. He was the favorite toy of a little kid who enjoyed her toys, Daisy being like Andy, and he was the leader of a small but loyal posse of other toys who would always lend a hand. On top of that, he has all the intelligence, resourcefulness, and planning skills of Woody. Where he and Woody diverged is their response to being separated from their respective owners, and arguably, what happened with their owners when separated. In the original Toy Story, when Woody and Buzz go missing and Andy finds out, Andy frantically searches for them until they return, and they never give up hope.When Lotso goes missing and Daisy finds out, her parents buy another Lotso and call it a day. This causes Lotso to snap and completely lose his faith in people. He then goes to Sunnyside Daycare, gathers allies, and becomes a dictator. If Woody had turned evil and bitter, he would've taken the same strategy: Gather allies, then gather power in anticipation of any upcoming threats.
Preceding Lotso is the Big Bad of the second half of Toy Story 2, Stinky Pete. Both he and Woody were part of the same toy series and shared similar apprehension about their longevity and a similar enmity to Space Toys. But while Woody decides not to abandon his friends or Andy, Pete will stop at nothing to get to Japan.
And of course, Sid was Andy's evil counterpart.
Chick Hicks, the main villain of Cars (also by Pixar) is actually the evil counterpart to Lightning McQueen. Both are actually portrayed as mean and arrogant racecars who cared about nothing but themselves and made fun of other cars. What makes them different is that at the end of the film, McQueen ends up losing the final race but is now respected by the other cars since he actually now learned to accept defeat by helping another racecar, Strip "The King" Weathers, cross the finish line after he was crashed by Chick, while Chick ended up winning the same race but is ultimately betrayed by everyone else since they found out about what he did to The King, and that doing such is actually against the racing code.
Also, Tigress and Tai Lung. Both don't know their real parents (one was raised in an Orphanage of Love, the other was a Doorstop Baby). Both only wanted their father/teacher's love. Like Tai Lung, Tigress believed she would be chosen as the Dragon Warrior by Oogway, and resented Po for 'stealing her thunder.' They also both suffer from Pride and a bad temper. Only the fact Tigress remained honorable and chose to become an even better and more worthy warrior (and, most likely, her defeat at the Thread of Hope) kept her from following the same path.
Po and Shen in part 2. Both have issues with their parents, both are real animals likened to mythical beasts (Po is the Dragon Warrior, Shen the peacock with his fascination with fire is clearly meant to be a phoenix) and they both have Failed Attempt at Drama moments.
The Princess and the Frog has Facilier (evil, male, tall, slim, young, attractive, slick) and Mama Odie (benevolent, female, short, pudgy, very old, hard of hearing and a goofball). Originally Facilier was supposed to be Odie's son.
In Titan A.E. it is revealed at the end of the film's 2nd act that Korso serves as this to Cale. Though he puts up a more amiable and hopeful fašade, he is actually just as if not more bitter, jaded, and self-centered as Cale is at the start ever since the destruction of Earth. Going so far as to sell out to the Drej. However, in the end after Cale refuses to let him die in spite of his betrayal, learning that the Drej are planning to kill him anyway, as well as the discovery of a way to defeat the Drej Korso comes around to redeem himself by giving his life to save Cale, his crewmen, and the human race.
Big Hero 6 Professor Callahan is this to Hiro. Both lost beloved members of their families and personally tries to go after and those who believed responsible in hopes of killing them. If it wasn't for Baymax's Thou Shalt Not Kill rule, Hiro would have gone down that same dark path.
Film - Live Action
The Shirley Temple flick Bright Eyes amusingly pairs Shirley with a bratty, mean Evil Counterpart little girl who picks on her.
Who Framed Roger Rabbit: Judge Doom to Eddie Valiant; both are law enforcement who hold a certain hatred towards toons. However, deep down, Eddie holds a certain fondness for toons, suppressing it mainly becuase of his brother's death and is still a good person underneath. Doom's hatred is perhaps more intense, which is ironic as he turns out to be a. toon himself.
In Kill Bill, Elle Driver, aka California Mountain Snake, is the counterpart to Black Mamba.
There are several examples of this trope in the James Bond series.
Scaramanga: At a million dollars a contract I can afford to, Mr Bond. You work for peanuts, a hearty well done from her Majesty the Queen and a pittance of a pension. Apart from that we are the same. To us, Mr Bond, we are the best.
Col. Moon from Die Another Day tells James that he based his Gustav Graves persona on Bond himself.
Rene Belloq from Raiders of the Lost Ark is a classic example. Both he and Indy are successful Adventurer Archaeologists with the main difference being that Belloq is willing to work with anyone, (including the Nazis) on a job, and that he's perfectly content to let someone else find the treasure, then steal it from them at gunpoint. Belloq also delivers an excellent example of a Not So Different speech at one point.
Ivan Vanko in the sequel is a better example. He's just as smart as Tony, and his father helped Tony's father build the first ARC reactor. Growing up in a Soviet gulag can't be good for one's personality. He ends up building his first portable ARC reactor in his rundown apartment. With his own box of scraps.
Both Justin Hammer and Aldrich Killian are played as "wannabe" Tony Starks who aspire to and try molding themselves after him to some degree. Both are, or become, powerful businessmen like Stark, and similarly to how Stark started out both are self-centered.
Captain America: The Winter Soldier: The Winter Soldier has many similarities to the Captain himself; both are soldiers, both have been empowered with science and both operate under orders of a larger organization (technically the same organization, as it turns out). Furthermore, both fought in World War II in the same unit but were cryogenically frozen (though Captain America stayed conscious after being revived, but the Winter Soldier was thawed and re-frozen as he was needed).
Push has two. Nick's counterpart is Victor, and Cassie's counterpart is the Triad Watcher. Victor is a better Mover than Nick, and the Triad Watcher is a better Watcher than Cassie.
It seems to be implied that Nick and Cassie are every bit (if not more) powerful, but are novices at actually exercising their powers compared to their more experienced counterparts.
That, and the fact they are son and daughter of the best mover and watcher anyone has ever seen (Cassie's mum set up events for ten years in the future) so they may have genetically inherited a bit of it. The agent pusher is also a counterpart of the experiment survivor, although she could arguably already be better.
In Star Wars, Darth Vader is naturally the evil counterpart to Luke Skywalker (a living incarnation of the evil that Luke is perfectly capable of), and Emperor Palpatine is an evil Force mentor version of Yoda.
In the prequel trilogy Yoda and Palpatine reprise their roles as Big Good and Big Bad masters of their Force sides and actually get to fight one on one. Their battle happens simultaneously with Anakin (now officially Darth Vader) and Obi-Wan's who became evil counterparts as the only confirmed living students of their respective Force sides and former comrades. In some ways it could be said that Dooku and Mace Windu were counterparts as well, though they never had a chance to fight, in that they were the public figure who acted as the right hand and enforcer of Yoda/Palpatine.
Star Trek: Nemesis had Shinzon, the evil clone of Jean-Luc Picard whose main purpose in the story is to show what Picard himself could have become had he grown up under more oppressive circumstances. Picard himself uses this in an attempt to demonstrate that Shinzon had the choice to become a better person, while Shinzon wanted to prove that Being Tortured Makes You Evil.
In the Heisei series, Godzilla gained an Evil Counterpart in Space Godzilla, a being created from a fusion of Biollante (who was a fusion of Godzilla's DNA and rose DNA) and a crystalline entity. While Godzilla was in neutral "force of nature" mode, Space Godzilla was definitely malicious and evil, coming to Earth to torment Godzilla and conquer the planet.
An even earlier example of this would be King Ghidorah, especially in the Heisei incarnation in Godzilla vs. King Ghidorah. Both started out as creatures (A Godzillasaurus and a trio of Dorats respectively) who got mutated by a nuclear/atomic explosion. However, whereas Godzilla became an unstoppable "force of nature" that can't be controlled (at least, not unwillingly), Ghidorah remained under the control of the Futarians (a group of people, and an android, from the future who wanted to prevent Godzilla's existence and use Ghidorah to destroy Japan).
In the Showa era, while both are giant destructive monsters, Godzilla destroys merely out of his hatred of humanity and will (reluctantly) ally himself with them against bigger threats to his territory. Ghidorah, on the other hand, merely destroyed cities (and wiped out life on planets) out of sadistic glee.
Destoroyah. Both were mutated by superweapons. Both have a breath attack. Both are semi-aquatic life-forms. The difference? Destoroyah is purely and utterly sadistic taking great pleasure in killing anything and everything in sight. Godzilla, on the other hand, will protect the earth (including the humans he hates) from greater threats.
Barbossa vs. Davy Jones and Jack vs. Beckett (his old nemesis) in the third.
Maccus, Mercer and "Quartermaster" are Evil Counterparts to Gibbs.
Bosun, also, in the fourth film is also one to Gibbs, and Blackbeard is this to Barbossa.
In Black Swan, Lily might be this to Nina. Nina frequently hallucinates a phantom doppelganger that seems to mean her harm.
This mirrors Swan Lake, the ballet the film is centered around; Odile the Black Swan, is this to the White Swan, Odette.
According to Jordy, the Bread-Squeezer is this to Jason in Mystery Team.
Glory has the Negro irregulars to the 54th Massachusetts.
Transformers: Dark of the Moon plays with this. Sam and Bumblebee are given dark counterparts in the form of Soundwave and Dylan. Bumblebee came to Sam for help, Sam's family having a history with Cybertronians. Likewise Dylan's dad received Soundwave as a "client", as the Decepticon had him crunch numbers to make further trips by NASA to the moon improbable, ensuring no one would ever find the Ark. This becomes a case of Fridge Brilliance in the final battle, where both human and Autobot kill their respective counterparts.
Dylan Gould: (to Sam) Do you really think you were the first one recruited to join the "noble" alien cause?
The former of the two like Bruce is motivated by the loss of somebody he loved, and thus sought justice and like Batman became a vigilante that goes past the limits of the law. Bruce like Ra's becomes trained by and a member of the centuries old vigilante organization known as the League of Shadows.
Scarecrow reflects Batman in how the manipulation and induction of fear are their primary weapons. Both also know and highlight the importance of using "masks".
Batman & The Joker are both described as having no limits. The former crosses merely judicial limits, the latter crosses limits that are moral.
Harvey Dent like Bruce Wayne starts out as good man with something of dark side that is trying to save Gotham City from the crime and corruption that cripples it. Both also share romantic interest in the same woman Rachel Dawes, as she has similar aspirations to them. Both Bruce and Harvey are specifically targeted by the Joker, who wants to both tear them down to "his level". While Batman ultimately resists, Dent winds up giving into it. After a great tragedy, Dent comes to the point like Bruce where he decides to go beyond the law. Working on the "Justice = Revenge" mentality Bruce had for a while before the death of Joe Chill that Rachel scolded him over. Going so far as to go after innocents as well.
Both Bane and Bruce were trained by the League of Shadows, and they're both Genius Bruisers. They both work in an elaborate underground base and they both live and die by their ideals.
Catwoman like Batman is a night prowler who dons the persona of an animal to enforce their own special brand of "justice", and uses means like stealth to their advantage. The two while talking to each other also relay the importance of their "masks". She is the only entry to this list however, who does actually come around in the end. Redeeming herself by helping Batman stop Talia's plan.
You could say that General Zod is this to Superman too or at least to a lesser extent. What with having the exact same abilities and learning to control his sensitivity to the Earth's sounds and atmosphere. He's even able to use heat vision later on in the movie. but other than that they don't have a lot in common.
The Jaegers and the Kaiju in Pacific Rim. Both are split into one through five classes and are so large that they need two brains to fully operate. Whereas the Jaegers are used to protect humans and the cities, the Kaiju are used to kill and destroy everything in their path.
Doc Holliday and Johnny Ringo in Tombstone. Holliday is Wyatt's lancer, Ringo Curly Bill's dragon. They are both highly educated, charismatic death-dealers and death-seekers.
Each installment of the Spider-Man Trilogy has a villain who parallels Spidey in some fashion:
Spider-Man: The Green Goblin and Spider-Man gain their powers as the result of experiments at OsCorp, and the Goblin even tries to recruit Spidey with a Not So Different speech. The key difference is that Spider-Man uses his abilities to help people, while the Green Goblin uses them to exact bloody vengeance on the people who have wronged him in the past.
Spider-Man 2: Much like Peter in the first movie, Otto Octavius is transformed into Doctor Octopus as the result of a Freak Lab Accident, and is subsequently motivated by the death of a loved one. But while Uncle Ben's death pushes Peter to become a hero, the death of Otto's wife drives him mad with grief and causes him to become a murderous psychopath.
To drive the parallels home, earlier drafts of the film had Octavius as a much younger man closer in age to Peter and Mary Jane.
Spider-Man 3: They don't really come much more straightforward than Venom, who has the same powers as Spider-Man and wears a black variant of the hero's trademark costume. Additionally, in his civilian identity, Eddie Brock starts off as a rival photographer who is employed by the same newspaper as Peter.
The Amazing Spider-Man 2 effectively shakes up the classic dynamic between Spider-Man and the Green Goblin by making Harry Osborn the Goblin from the get-go, and playing up his similarities to Peter. In addition the being the same age as Peter, Harry gets pushed into his Start of Darkness by the death of his father figure, and he eventually gets his superpowers from a self-inflicted dose of the same spider venom that gave Peter his abilities in the first movie.
Electro also seems to play a similar role. As the lost and awkward kid like Peter, but one who never grew up and thus sunk lower. Like Peter was earlier he is often bullied and is socially awkward to the extreme. Both also love and are skilled in the field of science. Both also go through an accidents that gives them superpowers.
Demolition Man: Simon Phoenix is this to Edgar Friendly. Both of them hate the emasculated, saccharine world deprived of human freedom created by Cocteau. Simon Phoenix, however, is a maniac who desires the freedom to create as much destruction and murder as possible, while Friendly believes in freedom to improve people's lives and guide them to their own choice.
In The Patriot Col. William Tavington serves this role for Benjamin Martin. A great deal is made about how he committed a horrible war crime during the French & Indian War, and later on shows that that dark side still has the potential to surface again in the scene where he ruthlessly kills a fleeing English soldier and later when he and his fellow militia men start shooting down surrendering opponents. Tavington's motives started with him trying to reclaim the honor and wealth that his father had lost him, citing that he can only get honor with victory and thus is the reason he started acting ruthlessly in his attempts to win no matter what. However as shown by the time the main events of the film he has come to enjoy the killing and war crimes he commits, completely submitting to that side of himself that Martin fears and wants to suppress. Then of course there is the fact that both are skilled warriors and army field commanders.
In Khartoum Muhammad Ahmad, the self-proclaimed Madhi, serves this role for Charles Gordon. Both are deeply religious and great military commanders who command the respect, as well as fear, of many around them. Both have also shown their willingness to resort to brutality if they feel it will further their goals for the greater good. Ahmad himself points this out to Gordon in the first scene they share together.
In The Shadow Shiwan Khan serves that role to Lamont Cranston, The Shadow himself. Cranston in his past was a ruthless warlord and drug dealer in East Asia until the Tulku took him in and set him down the path of redemption. It turns out that Khan actually idolized Ying-Ko, and he was the inspiration for him to take up his "birthright" of trying to live up to his ancestor Genghis Khan and become a warlord as well. The Tulku similarly tried to reform Khan, but it didn't take. Khan murdering him after he had learned what he wanted. Khan later tries to get Cranston to join him because of his past and their similarities. Because of his training with the Tulku he like the Shadow has supernatural mental abilities such as "Clouding men's minds" as well as telekinesis. (Something that Cranston doesn't manage to use 'til the end though) Both also have a network of allies in their service.
In Ang Lee's Hulk Bruce Banner's father David essentially serves as this to him. Even Gen. Ross makes a big deal of, and fears, the fact that both are geneticist that work on projects to try and improve and "toughen" the human body. After seeing what happens to his son David studies the effects and applications of gamma and eventually repeats the accident that created the Hulk on himself which also gives him superpowers as well. Though different ones, effectively being the Absorbing Man.
In Marvel Studios' The Incredible Hulk the antagonist Emil Blonsky progressively starts injecting his body with substances to increase his physical capabilities. By the end he has Samuel Sterns inject a compound made from Bruce's blood into his body which transforms him into the Abomination. Which in terms of size and strength is very much an evil counterpart to the Hulk. Blonsky also similarly becomes more aggressive as a result of his transformation.
It could also be said that whilst The Abomination serves as an Anti-Hulk, that Samuel Sterns was played as an Anti-Bruce Banner. Both were great scientists who worked on a project to improve the resilience and capabilities of the human body. Both of which eventually lead to their transformations.
In Jack Ryan: Shadow Recruit the main antagonist Viktor Cherevin plays this role to Ryan. Both are extremely patriotic men, who would do virtually anything in the service of their nation. In the scene where the two, as well as Jack's girlfriend Cathy, have dinner together we also learn that like Ryan Cherevin once not only served in the military like Ryan but also operated in Afghanistan in a "Different time, different empire - same graveyard." Both were also horribly injured while serving there.
Every film in the Expendables has a lead villain that serves this role to Barney Ross.
In The Expendables it is James Munroe. He is a mercenary completely out for profit, similarly to how Barney starts out. He even has a Not So Different speech he gives right before he is killed.
In The Expendables 2 it is Jean Vilain. Like Barney he is the leader of a mercenary group, his being The Sangs.
In The Expendables 3 it is Conrad Stonebanks. He along with Barney was one of the founding members of the Expendables before being disgraced and becoming a ruthless arms dealer.
In Troy there is a "trifecta" so to speak of character parallels that would fall under this. Centering around three groups of familial duos seen within the film.
It is ironic that in spite of their hatred for each other, Achilles and Agamemnon have some key traits in common. Though they have differences over ideals like Achilles' valuing of the soldier over a king (because they are the ones doing the physical fighting and dying to get things accomplished) whilst Agamemnon feels that the king is more important and thus deserves the glory (seeing himself as a savior who united a land of "fire worshippers and snake eaters" into a true nation). But their values align when it comes to how both are desperately trying to gain glory and immortality for their names. Something each puts above almost all else by the end. However, both do also highly value and deeply care about one of a younger relative. Achilles with his cousin Patroclus and Agamemnon with his brother Menelaus. However when said relative is killed, ironically in both cases the killer being Hector, they are sent into a belligerent, blood-lusting rage. Both also have a desire for Briseis.
It can also be said that Agamemnon and Menelaus parallel Hector and Paris as well. Both sets being royal brothers, the older of the two being the more successful and glorified of the two. The younger brothers are notorious womanizers and the ones who get into a feud over Helen, subsequently putting their brothers into positions to go to war. (though one of the two older brothers is clearly more okay with this than the other) In spite of anything however, the older brothers still genuinely care for their younger siblings. Whether it be tarnishing one's own honor by defending his life when he asks for help, or trying to get bloody vengeance for him after being killed.
There are also parallels between the duos of Achilles/Patroclus and Hector/Paris. While none of them are evil per se, they do fall into opposite sides of the conflict. Achilles and Hector are the older of the two, and each is renowned as the greatest warrior on his side as well as one of the greatest warriors who ever lived. Both are also respected military commanders. (Look at the Father to his Men section) Patroclus and Paris are one of their younger relatives who they are extremely close to. Both of whom are impulsive and naive, and find themselves deciding to rush into situations that they are not ready for. The biggest example being when they choose to go out into battle and go up against an opponent who is far out of his league. With both results, to varying degrees, leading to bad places.
Though evil maybe be a bit too strong of a word in Braveheart Prince Edward II effectively has this role to Robert the Bruce. As both are young men with the apparent destiny to become kings, and are also kept within the controlling grip of their father. Both of which slowly die from a debilitating illness. Where the two ultimately diverge however is that Robert manages to find both his strength and courage. Standing up to his father and then continuing the battle for independence in the stead of William Wallace. Edward's lover Philip tries to get him to similarly stand up to his father, and though he replies that, "I will stand up to him and more," he ultimately never truly does.