Fight takes place on the Cannibal Island Jack was on in the 2nd movie. Each get 3 days prep, and have limited intel on their opponent. Fight is to the death. 2 days into their prep, they are allowed intel on what the other's plan is, and are allowed to make changes to their plan accordingly. Who wins?
This is a very interesting match-up, I'd have to give the edge to the Joker as he's shown the obvious capacity to kill and has come up with some quite ingenious plans in the past. That being said, Sparrow is obviously quite a mastermind himself but seeing as he prefers to avoid confrontation rather than fight, I'd give this to the Joker, but not by leaps and bounds.
@PrinceAragorn1: Joker is the only guy in the world who can freak out both Batman and Superman, he's killed more people than they even had in those pirates movies, and I'm including extras here, other villains are terrified of the Joker, he even made Vandal Savage a bit nervous and the dude is freaking unkillable. There is literally nothing Jack has ever done to make me think Joker wouldn't just kill him before somehow using the act to piss off Batman