I do all my gaming on a laptop. Not because itīs "better" but simply because that is what I have. Vanilla SHIII works, but the constant roar of the fans when I play can get on my nerves at times...

The desktop wins the performance/cost comparison hands down, since most mainstream desktops will beat just about any mainstream laptop when it comes to graphics.
...But on the other hand: I play a lot of stategy games like Hearts of Iron 2 and Civ IV and these games run great on my laptop, so if portability is a perk you are willing to pay for and non gpu-intensive games make the bulk of your gaming... Well - go mobile!