Even ignoring the fact that the very definition of “acting” is portraying someone who is not yourself…
I'm just going to throw out there that the version of Joker in the comics that I like the best, the one I think of when I think of “The Joker”, is the version Heath played. The one who never tells his origin story the same way twice, the one who sees Batman as the Yin to his Yang and enjoys the never ending game he plays with him, the one who enacts devious Rube Goldberg plots to escape from jail or drive other people as crazy as he is.
In the Burton films, we see the IDEAS behind characters, we see their stories and motivations portrayed through a specific person's lens, skewed by the fact that the actors are clearly NOT the people they're playing. Their faces don't match, their personalities are different from in the comics…
They're not Batman and Joker and Penguin and Catwoman, they're "Tim Burton's Batman", etc.
In the Nolan films, we're given the REAL Bruce Wayne, Joker, and Two-Face…or at least as close as you could possibly get to fictional characters coming to life. Christian Bale looks exactly the way Bruce is drawn, he acts exactly the way Bruce is written, etc. Sure, the Batsuit is armor and Joker has scars and paint instead of falling in chemicals…but it's a far more accurate translation than we've ever had before or likely ever will again. As a reader of the comic books, that's what I want to see. I want the characters as I remember and like them, not loose interpretations.