Yeah...all the trends keep changing. Basically, you can only count on something so long as the current generation is out.
Here's the rundown:
1) ATI was bought by AMD a couple years back and the "ATI" moniker was phased out and replaced with "AMD" in 2010.
2) GeForce (Nvidia) and Radeon (AMD) both put out comparable graphics. The prices really compare to performance for current generation products. Last generation products (like the Radeon 5870 for example or GTX 480) can typically be found for less money than similarly performing current generation counterparts. But the current generation usually offers better performance/power draw and, occasionally, new features.
3) GeForce has had robust 3D support (using a $200 NVidia 3D package + ~$350 monitor) since the 8000 series in roughly Dec. 2006. Radeon only picked up 3D support with the 6000 series in late 2010. Reviews say it works very well, but the support is less clear, more 3rd party.
4) Radeon has had triple display support on a single graphics card since the 5000 series (fall 2009). GeForce still requires multiple cards for simultaneous use of more than two independent displays.
5) Occasionally a new card shakes up the price points or a temporary deal makes something a better choice.
6) Right now, Radeon has conceded that the GeForce GTX 580 can outperform all of their top single GPU cards. But Radeon also isn't competing at that price point.
For me, right now, I'd go with a Radeon 5870 (old, great prices) or 6950 2GB (can be unlocked to 6970). A few months ago, I'd have told everyone to get a GTX 460 1GB. But it all depends on your CPU, screen resolution, opinion of 3D, power supply, & budget. The GTX 560 Ti is an amazing card right now, but my personal preferences would have me buying a 6950 2GB.