I've read that it was Ledger who came to Nolan with his (Ledger's) interpretation of the character, and thats why he was given the part. Nolan agreed with Ledger's vision of The Joker as an anarchist.
I'm sure that Nicholson is perfectly capable of putting on a performance equally as creepy and unnerving as Ledger's Joker...one could argue he did so in The Shining. Nicholson simply wasn't asked to do that in Burton's Batman film, though. Ledger's role left him with a higher ceiling so to speak than Nicholson's role. You can only take a cartoonish villain so far, and Jack did a fantastic job. With this in mind, Ledger delivered something far more impressive in my opinion.
I really hope they don't bring Harvey back. With the way TDK ended I'll always believe the intention was for Dent to indeed be dead and for The Joker to return for the next film, playing on one of his trademarks in the comics that he can escape from Arkham Asylum seemingly at will. Obviously Nolan can't go in that direction now, so he needs to try to salvage a compelling story from a bit of a mess that Ledger's death has left him in. I'd prefer to see him move on with a new villain than to tell some sort of redemption story for Harvey Dent. Gordon and Batman have both confirmed Harvey's death, and already taken action in its wake. For me it would kinda cheapen the decision and the sacrifice they made at the end for Dent to just not be dead.