The 5970 has very similar average FPS to a GTX 580. However, AMD cards don't run as well as Nvidia's in BF3, particularly when MSAA is enabled. Also, crossfire may still be an issue in BF3 I'm not 100% sure. Either way though, $275 is a good price for a 5970, and it is a dx11 card.
Totally wrong, the 5970 destroys the 580 in BF3 and gets about the same performance as a 590, only a 6990 can run that game better. All the way up to 2560x1600 the 5970 will get over 60 fps average.