Is it any of the movies, live-action TV shows, animated TV shows or a particular run of the comic books that just screams Batman AND Superman, to you?
I think for Batman, I'm gonna have to go with the Bruce Timm/Eric Radomski Batman Animated Series from 1992. But Christopher Nolan's Dark Knight Trilogy is maybe a close second and James Tucker's Batman: The Brave and the Bold would be a distant third.
I think the Max and Dave Fleischer Superman cartoon shorts actually, probably best represent who Superman really is, but I guess a close second would be The Bruce Timm/Paul Dini Superman Animated Series from '96. And I suppose a distant third would be Man of Steel, and maybe even Batman V Superman: Dawn of Justice, if they take the time to flesh out the Superman characterization a little bit more.