A PC has a much better price/performance ratio, can be upgraded easily but require a bigger 'footprint'. A laptop can be carried around more easily, requires a smaller footprint but is more expensive and generally cannot compete with a desktop PC for gaming unless you pay silly money.
PC. laptop is mostly for portability. if you wanna play most demanding games on high settings then id recommend a PC with mid- high end GfX card and a capable CPU.
Get a desktop, much better in price and you can easily upgrade a desktop.
Laptop parts are more expensive and only a good idea if you travel allot.
Always buy a desktop for home use and a laptop if you travel allot.