There are so many reasons to vote for both. Jack Nicholson is an incredible actor with a nack for being crazy. He delivered the Joker with such mobid glee that his performance could never be forgotten. Heath Ledger, on the other hand, is an actor who was still up and coming before his unfortunate demise. He was a terrific actor, but his role as Joker was far beyond anything I expected from him. His joker was not full of glee. Rather, it was dark and morbid.
Unfortunately, in order for me to make this judgement, there would have to be some kind of similarity as to the heart of the character. I saw none. I don't compare the two and find no competition because the two styles are terrific and will always be in my mind.