Well aside from their performance, do you realize the difference, don't you?
Would you rather have a Corvette or a Camaro with a Corvette engine?
I don't think this is a fair comparison.
It's more like buying a car at the showroom or buying one online without ever seeing it. In theory the powred by ati should be comporable to the "real" ati's as ati is much more picky about who they sel theri chips to than other companies (cough, cough, invidia, cough). In practice, however, if you haven't heard of the company that's making the card then it might be kinda shabbie. On the other hand, some cards might actually be better than the "real" cards. The maya line from gigabyte, for example uses the ati chips but put it on a "hotrod" board for better performance. They also come with built in tweaking tools so you can overclock by using a simple application. I got one of these just to see how they work and I was very impressed, particularly in the fact that their drivers support hardware rotation!
Alsn is right in the fact that you might get screwed though.
So be careful, and if the price seems too good to be true then it probably is.