If you don't need the portability of a laptop, a desktop is the way to go, especially if you have spare parts. If you need a monitor, os, keyboard, speakers, mouse, then it'll be close between desktop and laptop on a low budget.
How much are you willing to spend?
Personally, I'd buy the y580, the 660m is a good bit more powerful than the 555m (3 gb is worthless as you will never go over 1 and maintain playability. If the y580 has the 1080p screen then definitely go for it. I think also there is the y500 on newegg for $899 which includes sli 650m (much much more powerful than the 555m).