The 6950 has slightly better raw performance... BUT my personal view is that nvidia has better drivers (though both these cards now have very mature drivers)
For me the 560ti is the better buy, especially at $40 less.. it really depends on the games you play and if they are both stock versions and the resolution that you play at..
At 1080, the 560ti is a good choice.. Higher res and the 2GB on the 6950 comes into play..
Also depends on the games you'll be playing.
If possible, stretch the budget or buy second-hand.. you'll lose quite a bit of money buying either of these cards new and then replacing in a few months.
MSI Radeon HD 6950 1GB Twin Frozr III Power Edition OC Review
Look at the stock versions of the 2 for comparison as they will both oc, the 560 oc's very well, not sure about the 6950.. There are plenty of reviews a few pages back in the video card section of the reviews.