Despite Nolan not trying to top Burton, I think he did because the Batman we saw in Begins is more Batman than the one we saw in Burton's film. I love the original but there are things in it that are fundamentally wrong and screw up the character, big time. The biggest of which is having the Joker be the killer of his parents, the second being the actual death of the Joker. Those two things are absolutely terrible. I'm not really talking about faithfulness to the source material in terms of being STRAIGHT out of the comics in every way, because Begins wasn't either. What I'm saying is that it stays more true to the characters in the comics-what makes them who they are.
I think Nolan is making better films AND better Batman films. What we see in Begins and (hopefully) in TDK is the closest thing to the comics Batman we've ever seen. Burton's movie was great, but not as great. As for the Joker, there are a million ways you could play the Joker and still have him be the Joker. Nicholson's was crazy, hilarious, and fun to watch. Ledger's could be completely different and still be the Joker. In the end, we win anyway.