Terry McGinnis was different from Bruce Wayne in many ways. Unlike his mentor, he had a childhood, and also faced the demands of a normal youth his age: a school career, his girlfriend Dana, and the responsibilities of an eldest son in a family which included his mother and his kid brother. In Amanda Waller's assessment, Terry may not be as smart as the old Batman, but he is every bit as devoted to helping others. A similarity between them is Bruce also had a mentor in Alfred to help guide him as well. The other difference being that while Bruce wasn't exactly gentle, he at least fought with certain rules. Terry on the other hand is completely willing to fight dirty much to the Joker's disgust. Overall, while Terry keeps the no killing rule, he is much more pragmatic.
Dick Grayson to Bruce Wayne as a a mentor to Terry. In contrast to the cold and demanding Bruce, Dick is considerably warmer, and advises Terry to make time for his personal life.
The Creeper a deliberate foil to the Joker, to the point where many things about him are set up as counterpoints — he is/was well known in Gotham as a reporter before his transformation to contrast the Joker's previous career as The Spook, he's a Lightning Bruiser rather than a Gadgeteer Genius, and he even has his own form of Joker Immunity... rather than sharing the Joker's uncanny ability to live another day, Ryder is outright Made of Iron.
Charlie Collins to Batman and Bruce Wayne, in that he actually does have a normal life and barely manages to hold onto it; whenever Bruce gets a sense of normalcy like marriage or family, circumstances manage to hold it off. Charlie has more mundane problems such as not having enough money for his children's braces and disliking his wife's meatloaf, and by the end he comes to prefer those to the madness that the Joker brings to any party. Batman seems to silently agree, given he doesn't call out Charlie for helping the Joker when hearing that the Joker kept Charlie as a "hobby." Unlike Bruce, he doesn't have to put on a mask to bring down the Joker.
Justice League: Superman to Batman, as per usual. They both have their own animated installment in the DCAU. Superman averts Deceased Parents Are the Best while Batman deals with Orphan's Ordeal. Superman won the Superpower Lottery and Batman is an exaggerated Badass Normal. Superman gave Lois an exclusive interview as his motivation was to alleviate public fears by ensuring that people knew where he came from and why he was here or, as his adoptive mother put it, so that people would not think he was like "that nut from Gotham City".
In "Hereafter":
Batman: I've got some things to say. I should've said them when you were here, but... despite our differences, I have nothing but respect for you. I hope you knew... know that. You showed me justice doesn't always have to come from the darkness. I'll miss... (explosion in distance) Batman: What did you always call it, Clark? "The Never Ending Battle"?
The Flash to the other Justice League members in season one. He is portrayed as still learning the full range of his abilities and being inexperienced in terms of sacrifice (his bewilderment over Wonder Woman’s banishment in "Paradise Lost" and inability to comprehend leaving a teammate behind in "The Savage Time" or in "Hearts and Minds"). Flash provides an interesting contrast when compared to his more seasoned teammates, who have been doing the job for years (and, in some cases, for centuries).
In "Tabula Rasa", AMAZO’s departure from humanity mirrors J’onn’s side story in this episode. AMAZO uses J'onn's power of Telepathy to read Luthor's mind, and decides to leave humanity behind. J’onn was also considering turning his back on humanity after seeing much of the overall selfishness and dishonesty among humans during his mind scan. Fortunately, J’onn had the chance to see the nobility of humans during the search for the lost girl. AMAZO had no such opportunity.
Superman: The Animated Series: Mercy Graves to Harley Quinn in "World's Finest". Where Harley is flamboyant and hyperactive, Mercy is restrained and precise. They don't get along.
