I agree, both are great adaptations of the comic that everyone should see. Like most of Tim Burton's awesome works, his Batman films have both a macabre and cartoon-like style. This fits Batman's character perfectly.
However, this is also the reason I prefer Christopher Nolan's vision of Batman. Unlike Burton's imagining, I could picture the events of Nolan's trilogy unfolding in real life. As cliché as that might sound, to me, that gives it a more engaging quality.
Christopher Nolan's trademark style is prevalent throughout his trilogy, but subtle enough for reality to breathe and let viewers easily suspend their disbelief. He's made the idea of a guy dressing up as a bat seem perfectly sensible.
On the other hand, Tim Burton's Batman seems more like it took place in an alternate universe. Not the DC universe either... but somewhere you'd be more likely to meet Jack Skellington or Ichabod Crane than Batman's superhero colleagues.
This is probably going to sound extremely blasphemous to true Batman fans, but Hans Zimmer's score is also part of the reason Nolan's Batman seems more engaging than Tim Burton's. As much as I love Danny Elfman's soundtrack, and find myself still humming his theme daily over twenty years after the first film came out, Hans Zimmer helped to breathe a new kind of life into the latest Batman with his scores. So much so, that other composers have been constantly mimicking the soundtrack's style since.
That's just a personal opinion. Both of these film series are a real treat (not counting the two by Joel Schumacher), and will provide timeless entertainment to both Batman fans and general movie fans alike.