About a year ago, I was deciding between 560ti and 6950, I settled on the 6950 2GB and never regretted. Extra GB of vram is better future proofing, and overclocks like wonders. http://www.newegg.com/Product/Product.aspx?Item=N82E16814102987
Free shipping and fits your budget and factory oc'd. I think thats an amazing deal. There is a slight chance you can unlock it to the 6970, just google it (the only difference was in the BIOS)
EDIT: And fyi, BF3 is known to use MORE than 1GB of vram already, although it might not be in your case since you like lower settings
but again, more future-proofing.
EDIT2: Oh, the price went back up... unlucky it was sitting at $199.