AMD a much better price/performance ratio in general, but a less efficient architecture. Intel has a more efficient architecture, but it's generally directed towards businesses, high/no budget gamers, and the rich kids. This might change with the new CPU's coming out next year, but as of now, Intel wins when it comes to performance only.
Also, Tasha is incorrect about more VRAM is better, it depends on your resolution, your amount of Anti-Aliasing, and your amount of Anisotropic Filtering. If you're running anything above 1600 x 900, I would recommend getting a gfx card with 1GB of VRAM. Anything lower than that, and 768MB is overkill. If you're one of those rich people who own a 30" 2560 x 1600 or 1440p monitors, then I would recommend you get a card with 1536MB of ram or higher.
Honestly, I would recommend either a
Radeon HD 6850 for 1080p or higher, or a
GeForce GTX 460 768MB for lower than 1080p.