1GB vs 2GB means more memory. Newer games (like BF3) are starting to use more of it. Back in the day, 1GB was all that was needed (you could even get away with 512MB's), but newer games are starting to use more.
It also comes in very useful if you plan to use Eyefinity. The 2GB's isn't needed on a single monitor, but like I said, newer games are starting to use more of it, so it's better to be future proof and get a 2GB model.
As with the 6950 vs the 560ti, this debate is always going on somewhere here on OCN. Comparing the 2 cards with the same amount of memory, they are just about even. 6950 comes out on top on some games, and so does the 560ti. After that, it just comes down to preference.
If I where you, I would go with a 6950 2GB model. There is a chance you can unlock and turn it into a 6970 for free. This isn't a 100% guarantee, but it's better than nothing.
6950's that I suggest looking at with the highest chance to unlock:http://www.newegg.com/Product/Product.aspx?Item=N82E16814102951
- Best Chancehttp://www.newegg.com/Product/Product.aspx?Item=N82E16814102945
- Apparently some come with a pre-loaded 6970 bios on the bios switch when set to the 2nd position.http://www.newegg.com/Product/Product.aspx?Item=N82E16814127562
- People have reported it successfully flashing to the 6970 bios.
Like I said, this is all chance, but since you have nothing to lose if your card does not flash, then you will not have lost anything.