In most cases it’s just a matter of which cooler they slap on it. Sometimes however, they do more than that. I have a Gainward Ati HD4850 which Gainward put custom GDDR on with much higher clockspeeds, as well as a decent overclock on the GPU. It outperforms a regular 4850 significantly. You should be able to find some benchmarks comparing the different manufacturers. Like I said it’s usually mostly a matter of temperatures and noise between the different coolers.
From software and OS point of view it shouldn’t matter which kind of video card you have. It’s exactly the job of the driver to take care of this. And when it comes to driver, in most cases the same driver is good for any video card with the same chipset. So, you should do just fine with your choise.
DISCLAIMER: I used words “shouldn’t” and “in most cases”, because there are always exceptions to the rule.
Drivers are supplied by ATI, not by the card manufacturer, so like Jarno said they should work for the same cards from different manufacturers.