OP, you can take a look at the test of my signature. I use a Q9550@4Ghz there, but I am pretty sure it has the same IPC as the PhenomII. So if you can increase your clocks safely, you can get a very decent graphics card.
No I am not suggesting you spend big for a 970, just showing what's possible.
Also since I am an avid supporter of raw video benchmarking, so people can have an exact idea of what I am talking about, here are some of my video links that may interest you. (spicy wallpaper alert on all videos

)
Grand Theft Auto V 1920X1080 V.High(-) 7950 @1Ghz Q9550 @4GHz -60fps
Grand Theft Auto V 1920X1080 V.High GTX 970 @1.5Ghz Q9550 @4GHz - 82fps
Star Wars Battlefront 1920x1080 Ultra 7950 @1.1Ghz CORE i7-860 @4GHz -60fps
Regarding GTA V as you can see the Q9550 paired with the 970, did show a performance increase and that with quite higher settings. Meaning that even a weak cpu can show quite good performance, when paired with a good gpu, even if it ends up being quite cpu limited. Just note that this test focuses on gpu performance and the game can get quite cpu limited outdoors, so apart from the performance numbers, I would advise you to pay attention on the outdoors portion during the last part of the benchmark.
As for Battlefront, I am actually showing you the 7950 there, so you can see that it can perform adequately. This is a single player benchmark however, so things in MP can get different regarding cpu performance and also gpu performance when things start getting crazy. For the record the 860 is quite a lot better than a PhenomII, but on the upside it showed very little cpu usage, also shown at the end of the video. I did play some MP on my 970 however and I didn't see a severe degradation compared to my
single player benchmark.
Going back to GTA V, cpu performance can be
greatly improved by reducing the shadow distance. I am getting 50% framerate increase on my Q9550+970 combination by this setting alone.
I will have to agree for now that Nvidia may provide better performance in some games, due to lower driver overhead, but since DX12 is here/coming, this may be irrelevant for the immediate future.
I would strongly advice to get another 4GBs of RAM. Also a graphics card with 3GBs video ram or more. So I'd start you start from the 7950 and move up.
Ideally I would advise something between a 970 and a 960, but there is no such offering from Nvidia.