How fast are you hoping to run BF4 at? If you're aiming for 60fps, ideally, you'll want at a 280X or a 780, but even then you might have to turn some options down.
Saying that, we really don't know how well the Mantle API will run until benchmarks come out (rather than marketing fluff from a pure AMD based PC), but you may end up being able to get 60fps at 1080p on Ultra with a 270X.