In film I would tentatively favor Nicholson's. I haven't seen the new one with Joaquin, but Heath's I'll say is more dark and brooding while the one from Suicide Squad (sorry can't remember his name) seems more manic. I can't remember the tv version role too well, and maybe it's its own separate category because the show was more light and a novelty. Any thoughts?
Hail Cesar! First and best. Listen, I was four years old. He left a big impression, and will always be my favourite deep down, along with West and Ward in their roles too. As for Catwoman there will NEVER be a sexier one than Julie Newmar.
That off my chest, I will say the character is a gift for an actor, and perhaps Nicholson is the last who might have had the wobbles on taking the part and therefore demanded quite so much of a fee (though obviously the star status of the actor makes him able to command such as is usually the case). I only say this because the rest are young enough for the comic book super hero stuff to not feel 'childish' to them and be more accommodating towards the role as a reasonably serious part.
I've only seen the main four so far, Romero - Nicholson - Ledger - Phoenix, and all being good actors they each excelled in the role. Not a bad one among them
But another who is a big contender is of course Mark Hamill who nailed it again and again in the Animated Series. I like to see these characters in episodes where they are up and running with the new story 'another day in the lives of', despite how entertaining yet another origin might be (there are of course multiple versions in the comics so it follows I suppose...).