Let's be honest, when it comes to certain characters, we like to think there's a standard for how they should be portrayed. This can apply to movies, television, video games, and more. With a character like Batman, who was done all that and more, it can be hard to nail down one "definitive" version. To me? I think it's fine that there isn't one, because Batman is really a multi-layered character. And each version we see (with a few exceptions) shows off a different layer.
For example, in the TV show Batman (now referred to as Batman '66) starring Adam West, you'd think Batman was simply a campy, pun happy Batman. But if you pay attention, you'll see not only is this Batman an absolute genius, but we get to see more of Bruce Wayne's character as well than in most other versions.
Then you have the Batman TAS/Justice League cartoon versions, where we got to see a balance between the intimidating caped crusader, as well as the detective that he's built a career off of.
In the movies, specifically, the Dark Knight Trilogy, we got to see not only a true birth of Batman, but the enduring spirit of him as he continually battled villains that brought him to his knees, only to see him rise back up again and overcome.
I recall a recent Batman Beyond short that was made for the 75th anniversary of Batman. In it, they did a wide pan shot of basically every Batman ever brought to viewers. As I saw them all, I immediately knew what made them all different aside from where the were from and who played them. And that was exciting to me.
Now true, everyone is going to have their favorite version of Batman. As you should! That's what makes us fans! But as for a "definitive" version? Well, that's a little tricky, because each version is meant to show off some different of this epic character, and who's to say that version isn't as great as another?