the only real difference is that one incarnation takes place in a film, which has to end, whereas the other takes place in comic books, which while rooted in the original incarnation, exists the freedom to reinterpret the character endlessly in and outside of canon (practically, since it's obviously way cheaper to make 100 comic books than 100 feature length movies, or at least much faster).
the nolan version contains a lot of elements from the various comic stories (especially The Killing joke), just brought to a logical conclusion because the film needs to make a definitive statement on the character, because they may never get the chance to explore the character in another movie because of box office performance, popular opinion, or of course, the unfortunate Actor Existence Failure, to paraphrase Tv Tropes.
as far as my preference, i'd go with Nolan's take, Batman Animated Series, and The Killing Joke.