Design wise, I love Burton's version. The Batmobile and the suit in particular. My favorite Gotham is Begins. It felt "gothic" but also a place you could visit. In a perfect world, Keaton would play Batman and Bale Bruce Wayne. Each had their strong suits. Bale was great as both in Begins, but the stupid helmet in TDK ruined it by squishing his face and making him a mouthbreather.
But besides the music, the design and Keaton, I just can't enjoy Burton's films as films. The stories are weak, the plots by the villains are ridiculous and honestly I find both of them pretty boring. With Nolan's version, I feel emotionally invested in what is happening on screen because we got such a great origin story for Bruce Wayne and why he is doing his war on crime. I care about the character and want to see him succeed. With the case of TDKR, even if Batman isn't in it a lot, I was still enthralled because Bruce's plan was turning to crap and it all looked lost for him, even though you know Batman will win in the end. With Burton's version, there is such a disconnect between Batman and the audience. We never really get to know the character of Bruce Wayne. The films are so much less about the most interesting character in these stories which happens to be the main character. In Returns, he is barely in the movie. I guess I just enjoy the approach of getting to know Bruce Wayne and having an emotional connection to wanting to see him succeed.