PC FPS is probably my second favourite genre and type of game out of everything and honestly, I don't think that an FPS is about feeling like you are the person you are controlling through the use of a keyboard and mouse.
If we were going for the most 'realistic' method then I think the Wii would probably win, but in terms of ease of play and most fun to use and be most competitive with, then the mouse wins hands down.
I think it is fair to say that a dual joystick joypad really has nothing on Wiimote and Mouse combinations.
Me personally? I haven't experienced good FPS controls using the Wii yet and I honestly don't know if I ever will... You can't lift and move the wiimote like you can with a mouse and it feels less direct and more messy on the Wii to me.
In terms of competition and fair competition the Wii Remote leaves too much open, and I don't think it is possible to be as competative with the Remote over a keyboard and mouse.