http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-10.html
at least try to get the GTX 570
Nice job cherry-picking the charts where the nVidia cards had the greatest advantage.
You might want to look at the other charts as well.
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-9.html
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-11.html
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-12.html
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-13.html
Or, you know, looking at the scaling info, since the OP is looking at a CF/SLI configuration:
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-16.html
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-17.html
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-18.html
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-19.html
http://www.tomshardware.com/reviews/radeon-hd-6970-radeon-hd-6950-cayman,2818-20.html
Oh, and not reading the conclusion (note that the resolution the article recommends the 6970 at is closer to the OP's desired resolution):
As for the Radeon HD 6970, it should be selling for $20 more than a GTX 570. Based on its display outputs alone, that makes AMD’s card worth the Andrew Jackson to me, personally. Otherwise, the two cards trade blows, with the GTX 570 faring better at 1680x1050 as AMD’s Radeon HD 6970 retains more of its performance at 2560x1600.
Note that some benchmarks even show CF 6970 outperforming SLI 580s (though it's obviously not representative of all games):
http://www.anandtech.com/show/4061/amds-radeon-hd-6970-radeon-hd-6950/15
To be clear, my recommendation would be to buy whichever SLI/CF setup provides the best value at the time you buy (possibly taking advantage of deals/combos/MIRs/whatever), whether that's 460s, 570s, 6950s, or 6970s. Just don't only look at one set of charts and expect that to be representative of the entire picture.
OP, there appears to be a FF XIV benchmark tool, you might consider seeing what other people have posted with similar-ish computers, though they're probably not running at your resolution.