I didnt read all the posts here (too many) but Nvidia DOES have DirectX 11 with the new 400 series.
Now I cant directly answer your question, because its not just about ATI or Nvidia is general. It depends on what requirements you have (e.g. gaming, video editing, home theater pc, etc), how much money you can give, stuff like that.
Both ATI and Nvidia have their bargains, but as for their latest series of cards it is like this:
ATI 58xx series cost a little less, draw less power, and are generally cooler than Nvidia.
Nvidia 400 series are faster, support CUDA, PhysX, and they have better quality than ATI.
I can give you a lot more details and point out the best card for your money, but you need to tell me how much you can afford to spend.