There are a couple factors. The X1800XT has more pixel shaders and (arguably) better architecture. This helps it go faster through big explosions and particle effects. It also has a better overall image quality, and that is debated too. The 512MB of VRAM, while not making huge differences now, will most likely have an effect in later games with bigger and more complex textures. Games like Call of Duty 2 thrive on the extra VRAM, so if you play that extensively, the X1800XT is for you.
The 7900GT is supposedly the better overclocker, and the extra pipelines should make it handle textures better. If you don't want to overclock, though, you can spend some extra money and get a factory OC'd one. In terms of noise, they are about the same, if not the 7900GT being slightly quieter. I'd go for an aftermarket cooler (but that's just me), as the X1800's is huge and the 7900GT's seems a little too small for the job. I can't wait till the Zalman vf900 comes out.