* good point, Gambit does not have the ability to throw virtually any object as a projectile like Bullseye... the 1st scenario goes to Bullseye, it's his forte... Gambit is disadvantaged...
* 2nd scenario is more balanced as the two opponents can use both their skills and abilities... i've read that a charged playing card explodes with the force of a grenade (correct me if i'm wrong), so i think whoever hits the other first, wins...
Bullseye has better aim of course, but Gambit doesn't really need to hit directly, and can throw a whole spread of them. Plus while his staff could block a thrown Bullseye card, Bullseye can only avoid, blocking's right out. Saturation fire is a nice advantage
Nothing but a deck of cards implies that Gambit cant use his bowstaff. Battle one would just be two guys throwing cards at each other until they both run out. I watch Mythbusters I know that they aint lethal. The best either could hope for is poking the other guy in the eye. Battle two is different. Gambit gets to use his powers therefore would have a significant advantage over Bullseye.