Also in TDK Heath uses knives and dresses like a cop, both nods to B#1 and #2. Also unlike Nicholson who was stuck with the ridiculous perma-smile make-up, Ledger's Joker was not always smiling (contrary to one of his "stories"
. Just like Joker in B#1 or TKJ was not always smiling either) and able to convey a much wider range of emotions.
Nicholson was actually pretty close to Romero's take on the character and even in a way to Hackman's Luthor, where back thyen playing a supervillain wasn't really taken seriously and meant acting way over the top like some kind of commedia del'arte buffoon or something.
Heath represents the spirit and the essence of the character.
Bottom line, the writing and the Joker in B89 simply aren't in the same league as what was done with TDK.
But to be fair, B89 did pave the way and prepared the audience for a darker take on the mythos.