What resolution are you running at? Normally, 2GB of ram only helps when running multiple monitors. However, looking on newegg, both cards are the same price so you might as well get the 2GB card and hope you can overclock it.
You can also get a Radeon 6950 for less (again, on newegg). The 6950 generally outperforms the gtx 560.
http://www.anandtech.com/bench/Product/330?vs=293