Mario got the game named after him (Super Mario Bros). He is obviously the dominant brother, while Luigi is the bumbling sidekick who cleans up what Mario doesn't get to.
I think that Mario would lose because he is really Cocky because he has princess peach and has beaten Bowser 20x. Luigi would win because he would use his wits and go around Mario while he was talking about himself and kill him, Luigi is Better to me because he actually seems like a real person.