I went with the X1800XT because I thought it was a better card than the 256mb version of the 7800GTX and because of the extra memory. I wasn't interested in SLI or Crossfire and both cards were roughly the same price prior to Christmas so it was a no brainer.
I would gone with the 512mb version of the 7800GTX, but that was drastically more expensive. Plus, I couldn't find any in stock to buy.
Bottomline is this: if cost is no concern, get the 512mb 7800GTX if you can find it. If the choice is only between the 256mb 7800GTX and 512mb X1800XT, I think the ATI is the better choice.
FYI, the fan is no where near as noisy as all the horror stories I've read. Just make sure your case has good ventilation. So long as the hot air can get out, it'll never have to spin at full speed (even under load).