Saw that too deal,i swore the package said it was a 2gb,but heck for all i know perhaps both the 1gb and the 2gb were the same price.
Doubt it makes a difference,getting quality smooth gameplay in some titles like BF3 would require dropping enough settings as to where vram usage settles under 1gb anyways.
Running my 7850 at 1920x1200 with all medium in BF3,no msaa and post aa on high with hbao boosts a max usage of 733mb in a 2 hour session while giving me my bare 60 fps+.