ATI pretty much has the better price for performance cards right now. I have a 5850 that I OCed to be comparable to a 5870, and I can tell you Crysis works great at High detail 1920x1080 4xAA, but at Very High it's just not powerful enough for acceptable FPS levels (works ok but with slow downs whenever there's some decent action). If you want to save some cash, consider crossfire 4770, otherwise a 5850 is going to be better. Nvidia's got some decent ones too but you'll be paying more. I think their GTX 280 is quite good but costly... IIRC it's around the performance of a 5870 (or maybe between 5850/5870). Anyway, we're getting into the $450 price range with high end cards so a really good question is: What is your price range?? If it's unlimited, go buy a 5970 because it's the single best GPU (actually, 2 GPUs) you can buy right now ($700+). The 5850 is around $300 depending where you go and which model you get.
EDIT: If you haven't checked, read this http://www.tomshardware.com/reviews/graphics-card-radeon-hd-5870-geforce-gtx-480,2621.html