You can certainly run them on high at 60fps+. Also Im pretty sure you can play on ultra but probably on all of those games, probably with one or two things turned off. I dont know about arma 2 since i've never played it but read that it is badly coded. I play bf3 on high with some settings on ultra and it never goes below 40fps on big 64 player maps. This is with a 560 ti 1gb.
EDIT: Forgot to mention that the 560 Ti is nearly on par with the 6950 but the 6950 has better specs. Also your version has more memory allowing to use anti aliasing (which the detail can only be spotted by people with eagle eye view detail)