I think Ledger had the greater challenge. Ledger had to take an iconic character and do something different to the style of Cesar Romero's, Jack Nicholson's, and Mark Hamill's takes on the character. No easy task. Not to mention he had huge expectations of him from millions of fans across the world to do their beloved character justice.
Not only did he succeed in playing the Joker in a wonderfully unique way that had not been done before, but I think by and large he surpassed expectations of the fans and audiences.