here are the benchmarkshttp://www.anandtech.com/show/4137/amds-gtx-560-ti-counteroffensive-radeon-hd-6950-1gb-xfxs-radeon-hd-6870-black-edition/5
you will see the 1gb 6950 will equal or sometimes outperform the 2gb 6950 in the 1920x1080 tests.
there are some gains to the 2g 6950 in the 2560x1600 tests.
so unless ur gaming above 1080p (eyefinity or studio quallity monitor) there is no difference you will see. infact if anything the 2gb would be a little slower.
this is based on current games released anyway.