Good point about the strafing (sic). I should find the source for this, but there was an online multiplayer competition done between PC Halo players and console Halo players and the PC guys stomped them, because 1. Hotkeys 2. More accurate, and faster look ability with a mouse. Feel free to tell me I'm wrong, because so much of this is subjective.
But, there is one type of game in which the mouse and hot key setup is far superior: real time strategy.
It's also better for turn based strategy as well, imo.
Controller = platformers, shooters, fighting games, kboard/HOTKEY/mouse = stategy, FPS and most RPGs