Supposedly there is no difference in performance because any additional RAM requirements will be sent to the system memory and most people playing BF3 will have at least 4 which should be able to handle any spill-over. I recently received a 3GB GTX 580 and the extra memory may not be making any difference but BF3 on the highest settings at 1920x1080 uses anywhere between 1600 and 2200 depending on the level and amount of players. If you are not on a budget then the 3GB may be worth it.
Have you considered waiting 1 more day for the HD 7970 which is only going to be released with 3GB of VRAM?
I know you have the one single display but if you ever do more than one display you will bw glad you have the 3gb version since the extra vram comes in handy with multiple monitors. Since a game like BF3 is so gpu demanding , then cards with more then 1gb of vram will do better and give better perfomance.