I believe if you have a favorite console (which I believe saying everyone does is a sound observation) then you feel some pride in the fact your console has games that another doesn't. However, most people don't base their favorite console on name by itself. Halo fans love their Halo while InFamous fans love it. People initially liked their favorite console because of the games in most cases. So if they were switched then they would probably move to the other console.
Counter argument: yes, they would flip-flop in their hate/praise because a lot of people started out with 1 console. That console had its exclusive games that the people played. Because they had those games and not others, they started liking those games more. For example I got a PS3 with God of War. It was one of the few games I originally had. Because of that I really enjoy God of War. If I would have gotten an Xbox 360 however, I would have probably gotten Gears of War and therefore enjoy it more than I do now (not saying I don't enjoy it). And I wouldn't have been playing God of War as much so I wouldn't enjoy it quite as much.
I feel like there are too many variables to your question. Is this a sudden switch at the current moment or a switch at the very beginning of the generation? If it were a switch at the beginning of the generation, I feel Sony supporters would still be Sony supporters and Xbox fans still Xbox fans. However, if they switched right now then I believe most people would stick with the games. (This is assuming most people's console preference comes from games and not other factors and that they significantly like one's games over the other).







