According to Word Of God, A:TLAR will also display the similarities held between Deuteragonist Katara and Azula, as the original series did with its protagonists (Zuko and Aang).
In Winter War, Urahara notes that he and Mayuri are really very similar in their desire for knowledge for its own sake, and that the only thing that keeps him from performing Mayuri's experiments is that, unlike Mayuri, he likes people and wants them to like him back.
A Protector's Pride has Byakuya say this about Ichigo and Yamamoto despite their dislike of each other. Both will fight viciously for their beliefs, goals and True Companions. Byakuya however notes that this must hurt Yamamoto more since Ichigo might remind him of his younger self but years of compromise and dealing with the (corrupt and xenophobic) Central 46 made him Lawful Stupid whereas Ichigo didn't cave in despite Yamamoto acting like a Obstructive Bureaucrat to him.
"But what do kids know of strain, anyway? They don't know a thing. They just play all the time. Even their work is play. Not like your work. Your work... is work. Isn't it?"
Also, he tries this with Monkey Khan since they have a need for revenge.
In Connecting The Dots Hinata finds a kindred spirit in Lois Lane while Lois describes Superman in a way Hinata finds familiar. Readers also get to see that Superman and Naruto are also not that different during Lois' description of Superman.
Lois: "He just has...something inside him that compels him to help people."
Robin is Sasuke minus the need for revenge.
In An Entry With A Bang!, it is noted that Clancy-Earth and ComStar actually have some rather similar goals.
Connection has the example of Lirin and Ayaka having similarities between themselves.
In Kyon: Big Damn Hero Kyon realizes this and mentions it to Wataru as both want to protect their loved ones, in particular each one's sister.
Lecture for Moo Moo has Woody admitting to Moo Moo that she is going to a similar case to Lotso as both of them are abandoned by their owner by accident, not going back to them, and they're oblivious to the fact that they're the abandoners, not their respective owners. He successfully convinces her not to become like Lotso.
Renamon Who has Valmont admitting to Rika they're so alike. Both of them are rich, have a spoiledattitude. That second statement reminded him when he was once a kid and still has it as an adult. Neither of them treat their non-human partners right; as a result, they lose them. As much as Rika said she doesn't need Renamon and that she hates Digimon, Valmont shares those same feeling with Shendu. When Rika tries to deny those, she eventually realizes Valmont is right; she has become like him.
Similar Case: Vegeta admits that he isn't too different from Eas. Both of them are cold and stubborn, trying to prove their worthiness to their bosses, trying their best in defeating their rivals who are always stupid, grinning, and carefree, and losing their cool when they showed them to be better than themselves. After her battle with Cure Peach, she finally understands that she is not so different from him after all.
In When There Was A TomorrowShepard and his crew can't help but see an uncomfortable number of parallels between The Illusive Man and Dr. Halsey, and several of his teammates seem to be losing respect for him for siding with her, maintaining loyalty only because Shepard thinks she's their only ticket home.
In Depravare Kira and Righteous (Light and L) have always readily accepted this about each other and are offended when Near doesn't get it, he doesn't want to see Kira as anything but an evil mass murderer and his mentor as anything less than a saint.
In the Uplifted series, it is an overall theme of the stories. To the average grunt, the World War II wasn't that different irregardless of who you fought for, as seen during the Invasion of Malta with Rommel's troops. Seen particularly in Skorzeny and Churchill.
When Celestia and Discord meet each other again for the first time in Act II of the Legends Of Equestria continuity, it's because Celestia is summoning Discord's magic to make herself more powerful. Moreover, Discord reveals to her that he was once a unicorn like her, before he accepted dark magic as a way to get his life back.
In Act IV, Discord reveals that he is in fact Celestia's great-great-great-grandfather.
Rainbooms And Royalty: Just before the Final Battle, as part of her pitch, Nightmare Moon pulls this on Rainbow Dash, saying that she knows what it's like to have one's self and achievements overlooked in favor of another. Dash, however, doesn't buy it.
In All-American Girl, despite being raised as a human and not a pony, DJ clearly shares a temper and obstinacy with her biological mother Rarity that is all too-well noted by just about everyone/everypony who knows either of them.
Hit and Hug has Rainbow Dash admitting that she's not too different from Fluttershy since both of them are arrogant and realize the error of their ways to make amends with their friends.
The rather odd Team Gai (Naruto, Hinata, Lee) from Geniuses of Hard Work puts three Determinator's who are considered weak for being differenr with two being considered "dead-last".
The reason why the team of Hinata, Naruto and Shino from Team8 is so popular. All three are discriminated/hated/mistreated in some form which leads to a rather close-knit team.
In the last scene of The Second Try, Shinji admits he finally understands his father a bit, since when he thought Asuka was dead he almost started the Instrumentality right on the spot. And he would have done if Asuka would have not reached him in time.
Kaworu taunts Asuka stating maybe she knows him better than she admits.
In the Portal 2 fanfic Test Of Humanity, GLaDOS uses this to torture Wheatley by telling them they're no different from one another.
"Oh, but it's true. Face it, moron core, you are nothing but a cold, heartless, sadistic, unloving machine. Just like me. You may look human. You may sound human. You may act human. But that's only because I wanted to see how long a robot could live a lie. You're more like Hal than you want to admit. You're more like me than you want to a-"
In Tengen Toppa Gurren Solvernia, Nia undergoes through a small Heroic BSOD in the beginning, after realizing that the beastmen are people just like she and other humans are. It's part of her inner conflict to protect herself and her friends and trying to make peace with the beastmen.
Nia: I don't understand... if they're like us, then they wouldn't have any reason to hate us, would they?
Others
In the fanfic Camp Scare Abby realises, due to her traumatic childhood, she's Not So Different from the children she was being a Jerk Ass to.