Well, it is 2 completely different takes on the character when you get down to it. The only thing the same is the name really.
Jack's Joker (to me) was the comic Joker that had existed up to that point. His interpretation of that, in my opinion, was spot on and is easily my favorite live-action portrayal of the character.
Nolan's Joker was the character as told through a "real world" setting, and not a comic book fantasy. He was a psychotic anarchist... something that could exist in our world (and does, though maybe not on that level). At portraying that, Ledger did a fine job... and if that is the version of Joker that one prefers, that is fine.
But it really is apples and oranges. It doesn't just boil down to a better actor, or which performance you prefer... One also has to account for the fact that they are 2 radically different things that are both called "Joker". If I were asked which one was the better "comic book Joker", it would be Jack. If I were asked which was the better "realistic Joker", it would be Ledger.
Once you get into that, you have to decide which film setting you prefer overall- Burton's comic fantasy, or Nolan's real world crime drama. I prefer Burton's world, so therefore I'd prefer Jack's Joker, as that is the series I prefer... but that is just me. I won't disparage others for choosing the latter....
Sallah
