1) wrong forum. There is a
Video Card & Graphics forum
2) Neither is "better". They both make multiple cards aimed at similar specific price and performance points, in direct competition with each other.
3) List your hardware specs. You might be bottlenecked by your cpu, etc
4) at the $200 price point - You're probably going to be looking at maybe the cheapest GTX 560Ti or a Radeon 6870. You might be able to find a Radeon 6950 1GB for that price, but I would probably advise against it and get a 2GB model instead. Likewise, a GTX 570 can be had for a little more as well.
5) Radeon cards do no do PhysX. I don't want to start a battle over that but if you are buying it for B:AC, then check the benches & reviews for the PC version of the game and see what effect PhysX even has. If it makes a meaningful difference, then you'll probably want to get an nVidia card, as the workaround for Radeon cards is to run a dedicated nVidia card for PhysX anyway.