Yeah, that's a really, really horrible graph. Really horrible. The information as presented is still mostly--
Dear god that that is a horrible graph. No, really. That's almost criminal use of statistics. The guy who made it should be slapped with a herring. Wait. That's from AnandTech? Oh, I see, now. They were never meant to be compared together. It's Anand's grand compilation of benchmarks in compare mode. Still... its a bad presentation.
Let's ignore the bars. They are dumb. The numbers are fine. The 560 is a strong card, which gets some strong benefits from its CUDA cores when handling textures. However, it is limited somewhat by its memory bandwidth and number of pipelines. As such, it does really well at "standard" resolutions, but it slows as the resolutions grows and its pipelines/shaders struggle to keep up with the increased screen size.
The 6950, on the other hand, is a very powerful card that lacks the parallel texture processing of the nVidia's Fermi architecture. It is really tuned for higher resolutions and levels of anti-aliasing. Notice how the increased resolution really doesn't impact the frame rate. You can really push loads of pixels through the card, but it gets stopped up a bit doing the texture work.
Now, the one missing piece of information here is the date. When the 6950 was originally released, I'm pretty sure AMD had a serious issue with their drivers that was crippling it in texture-heavy games, and particularly Civ V. Since then, the drivers have improved and the performance went up. I don't think that it will match the 560 Ti at 1680x1050 (the 560 is tuned for that resolution), but its going to be good enough. Would you really care about the difference between 60fps and 55fps?
To be honest, the cards are really pretty close, so close that you're not really going to notice a difference between them, even for other games. The 6950 does have the edge overall. Both can overclock, but they both overclock to similar levels, so there's no real advantage to either card there. The 6950 is selling for $230-$240. The 560 Ti seems to be selling for $220-240. Myself, I opted for the 560 Ti, due to the only two things that is really different: Heat and Noise. The 560 Ti is the cooler and quieter card pretty much across all models. However, I recognize that lots of people simply don't care about those things.