Braid being a port of an Xbox exclusive game is most definitely compatible with a gamepad.
Mass Effect doesn't support one on PC.
As for which game? Pretty much any game, except the few that don't support it. And the only games that are better on a console are the exclusives - as you can't play them on your PC! I have both a PC and an Xbox and there's no contest - PC all the way!
Assassin's Creed 1+2, Dead Space 1+2, Batman : AA, Borderlands, Darksiders, DeathSpank + ToV, Lara Croft and the Guardian of Light to name a few

They all work very good with a game pad and offer a better experience - higher resolution graphics, high AA, high textures, 60FPS = win
