The reason I went with the 570 is that I read that Arma 3 is being made to utilize PhysX which would give the edge to the 570. Am i wrong?
I can't comment on the PhysX thing, but if you are going to be playing at 1080p then the 2 Gb of vRAM on the 7850 will make a noticeable difference. From my experience, the 7850 can still max out games which are meant to be tuned for Nvidia cards (Batman Arkham City, Crysis 2).
Both are great cards, so get the one which suits your needs.