I hear that the Xbox version of HL2 is horrible. The PC one is amazing though.
I've played both, and both have advantages and disadvantages, depending on what your comp is like. If you have an old, outdated comp, get hl2 for xbox, it is a great game, but you don't get DM, and you don't get near as many cheats. But if you also wouldn't get any lag like you would on your computer. If you have a good computer, get the game of the year edition, with Hl1, Hl1DM, HL2, HL2DM, CS and then you can download GMOD too, and thats hella fun.