I'd take losing 6-1 6-3 cause either way its a loss and I don't want to waste so much time and energy losing 12-10 in the third set. I'd be so mad with myself too that I lost so narrowly, in a nut shell to spare myself excessive emotion, 6-1 6-3 is the way to go.
I'd hate to lose either but I think i'd rather lose the 6-1, 6-3 actually. I think that when I lose a match like that I don't really get so down on myself, because it's usually a case of nothing working for me. Everyone has their days like that. But to be so close, like a 12-10 loss at a slam, I would be emotionally distraught I think, lol. The lopsided score I'd get over quicker.