Movie Bullseye vs movie Joker

A gang war erupts, Falcone hires Bullseye (Colin Farrel) to hunt down and kill the Joker (Heath Ledger).

Who wins?

If Bullseye ever got Joker in his sights, Joker'd be good as dead.

Bullseye lolstomps

If Batman barely did it and he's a billionaire Bullseye ain't catching Joker.

To hunt down The Joker? I don't really think that'd be hard considering the Joker's MO, but if they ever came in contact with each other, I don't see what's stopping Bullseye from pegging Joker a couple of times in the head with any sharp object before he even realizes it.

Bullseye. 10/10

Bullsey ftw

Bullseye kills him with a marble. Nolan Joker wasn't really a fighter.