I play League to have fun -- something that is not directly equated with winning in my mind. I would pick the unskilled but nice player every single time, without exception. At the end of that game I may have lost, but I will have had fun doing it and will have been working with players who want to work together as a team and who are legitimately trying, even if they're awful. That, to me, is a lot more fun than winning a game where someone spent half of it shitting on someone else for not living up to their expectations.
Hell, some of my most memorable games (and some of the most fun players on my friends list) have been from games where we got stomped so hard the game became "let's try to kill just ONE tower" or "if we kill Twitch we can call it a moral victory, right?" When we're all laughing it off and having fun the DEFEAT pop-up at the end means basically nothing compared to the enjoyment of that game.
Losing is a part of League, and always will be. Being an asshole doesn't have to be a part of League.