
While the superhero movie received almost unanamious praise from everyone, the best compliment was reserved for Ledger's performance, with many saying that it was much superior than Jack Nicholson's version.
After catching the movie, here's my take - there really is no basis for comparison as both actors fulfilled what was required of their version of the Joker within the context of each film.
Tim Burton's Batman was the first onscreen adaptation of the Caped Crusader, following the "good guy versus bad guy" format and retaining a comic feel. In that sense Nicholson delivered brilliantly, giving an over-the-top performance contrasting against the Michael Keaton's brooding Batman.
In The Dark Knight, Christopher Nolan reconned the franchise by giving it a gritty, realistic reconstruction which feels more like a crime drama reminiscence of The Departed. It's similar to WWE's transition from the Hulk Hogan "Golden Age" to the "Attitude Era". As such the Joker had to be adjusted to this new setting. Ledger's sinister performance, in my opinion, was great but he was greatly aided by the script's theme which tackles the issue of moral dilema involving Batman, Joker and Aaron Eckhart's Harvey Dent (which I think IS the soul of the film - take away Harvey Dent and the film would have revert back to the "good guy versus bad guy" format).
In short, both are tailored according to the film and would have been outta place if they had swapped films.
Final verdict: Draw