When you're challenged to a duel in Red Dead Redemption, it's easiest to draw the instant the screen says "Draw!" and go for six headshots to snag the win. If you really want to feel like a badass, though, you have to keep your gun holstered until the other guy draws his, and then target his hand before he can kill you.
It's incredibly hard to do, but if you can manage it, you'll blast his gun right out of his hand and get double Honor/Fame for winning. And, of course, you will inevitably end up saying "That was awesome", because it really is something to behold.