I'd say Max Payne is better on the computer because on the level with the fire it is hard to beat on the PC but easy on the Xbox.
And for Halo being different than Counter-Strike, Halo is set as more of an alien vs human theme while CS is a terrorist/anti-terrorist them. You can fly on Halo in some of the vehicles too, and you get tank too in one of the levels.
I don't see much a difference of Morrowind on the PC except you can edit the scenary or something... Unless you have a joystick on the PC, I would say get it for the Xbox.
Games you should buy/rent:
Halo
Max Payne
Morrowind
Spider-Man
THPS 3
DOA 3
Transworld Surf
Games you might want to look into:
Star Wars Jedi Starfighter
Star War Obi-Wan
NBA 2K2
NFL Fever 2002
NBA Inside Drive 2002