Pizza eating duel?
Horror movie knowledge duel?
Amount of breasts touched with permission duel?
I'm guessing you were hoping for a more traditional answer. I'm definitely a sword guy, if that's your angle. Guns are messy. They miss, and when they hit, it sucks hard. Swords are elegant, and there's no weird smell when they deliver a fatal blow.
Of course, two modern assholes with no sword fighting ability wouldn't possess much elegance. Just as well have a pool-noodle duel as expect grace in that situation.
Short Answer: I don't care so long as I get to say, "I'm not left-handed."