It's far, far easier to play a psychopath than a possible paranoid schizophrenic descending into a state of mental collapse - one role is there for the actor to have fun with and is full of expression, anarchy and mischief, the other is restrictive, binding and has to be plausible due to the sensitivity of the subject matter.
Psychopaths tend to be enthralling, charasmatic and perfect cinematic matter: they are larger than life, wild, uninhibited, unrestricted and everything is mostly outward (or expressed in due course) and there to be easily ingested by the audience. Better still, they are incongruent, which gives the actor massive scope to perform within. Ledger gave a stellar performance, but his remit was so much easier as, to me, to be incomparable.
As I said in my initial post, they are such different Jokers, I wouldn't even begin to pair them off. Perhaps, if there is a follow-up and Phoenix is allowed to be a more sociopathic Joker, we (I) can draw some kind of similie.