If you are looking to run BF3 on all Ultra settings at 1080 resolution you need a dual GPU setup, period. I have a slightly OCed GTX580 and run everything on High except Ultra details. A 5870 will probably get you in the Medium and High combined settings. The best thing you can do is just set video settings to AUTO. It actually does a VERY good job of choosing settings. Just turn on VSync. AUTO gave me the settings I have now. I've tried creeping them up a little, but ultimately ended back to where it was.
BF3 on Medium settings with DX11 still looks freaking amazing. It is one of the best looking PC games to date.