The actual chip is the main factor in determining performance, but no single factor determines what's better.
The best thing to do is research the card(s) by looking at benchmarks, and/or by asking someone who knows.
There is a graphics car FAQ article
here which should provide a good starting point.
As for your video card, I would recommend an 8600GT, it's fairly cheap and would have equivalent/better performance than your 6800GT.
