Which of these 2 gaming desktops are better?

I'd get the AMD one... The Celeron can't handle high end tasks. A Celeron is one of Intel's mainstream CPU's stripped of cache, instruction set support, and other technologies to sell for cheap. As what Peter said, neither of these are gaming computer due to the lack of a dedicated graphics card. If I were you, I'd save for a Radeon 5770, but that's like $150. If you are too cheap (or poor) for a decent graphics card, then you should (at the bare minimum for gaming) get a Radeon 4670, which is about $70.