The ATI equivalent to the 6600GT would be the x800GT.
Read this review: http://www.hardocp.com/article.html?art=ODA5
I learned so much from this article in the first 6 paragraphs. Not only did I learn about these two cards specifically, but video cards in general and why one card is better than the other. (Bigger isn't always better.)
Even if you're not looking at these two cards specifically, I would encourage anyone who's in the market for a new video card to at least read the first 6 paragraphs of this article.