at 1080p or less the gtx560 performs similarly to the 570. go with the 560ti. If i were you i would seriously look at overclocking your CPU to at least 3ghz, it shouldnt be hard.
I agree with Mactronix; either of those cards would be good. Check benchmarks for the specific games you play to decide which one you want. I believe the HD6950 is generally a little stronger, but there are some games (e.g. Civ V) where the GTX560 blows it away.
Thanks guys. I will most likely stick with nvidia as I'm really happy with them. Is there any cards that wouldnt be able to run on my CPU? Maybe of I'm feeling a little more generous money wise?