well assuming it was only morality thats reversed it would really just come down to which of us became aware of the other first, otherwise i would win without question assuming standard values and bases for those values. obviously i would appear to be the evil twin, because knowing me if i was just a hair more evil i would always pretend to be good, and if i was a little more good i probably wouldnt be such a horrible *****.
unless of course i was in *that* sort of mood. now that i think about it im not sure i would be able to resist even if i wasnt in that sort of mood or even slightly into that sort of act that day, just to say i had done it and possibly take high quality video as proof. afterwards there might be a bit of awkwardness and there would be either a mutually agreed upon duel (either foil or something highly explosive and likely to kill us both, along with any video evidence) or we would cooperate and either conquer earth or do the whole superheroism thing, depending on which of us was which(and i would be interested to find out, im curious but i dont particularly care and i think i just answered my own question there didnt i?)