Halo 1 and 2 were the same way on PC. Halo 3 is built specifically to play on the 360. Whenever games are built to play on a platform other than PC they always play worse on PC, unless your rig is far superior to the console.
Umm never played the Computer version of halo 3 but i could see it being a good thing. I played the original on the xbox and on the computer. In halo 1 i found the computer version better to play. I could aim better because mouse is more accurate. To play on the computer your would have to have a good computer for it to make to big of a difference. It all comes down to... Which one i feel more comfortable with. A controler or a keyboard.
Hmmm, I would say 360 ONLY because im the only one of my friends with a good computer that could play it lag free. I play single player on PC for mods and console commands, and multiplayer on 360 so i can play with my friends online.
I prefer it on Xbox 360 where you have all the controls in your hands instead of being spread out and pressing different number or letters (etc.) around your desk.