How would you compare the Joker as depicted in the Dark Knight with other incarnations of the same character from distinct media (specific movie, TV show, comic)?

Do you think the TDK Joker is meant to be comic or funny, when compared to other incarnations? Is he meant to be more or less violent? Would he ever be able to "take over" Gotham in the way that other Joker incarnations might, particularly considering his lack of loyalty and care for his henchmen/underlings? Any other thoughts?

I just rewatched the movie for the first time in a few years and it's hard to find discussion about TDK Joker that isn't "Look at this crazy theory about TDK Joker being the hero/romantic lead/wisecracking supporting character of Christopher Nolan's The Dark Knight!"