Well first of all, it's no longer ATI, since AMD bought ATI and all the cards are now produced under AMD brand.
But on to your actual question. You're not going to get a unanimous response. Both companies make some really really good video cards.
Chances are, that if you get high end card from either of those companies, you'll be able to throw in just about any game at it, set it to max graphic settings and not have a glitch (assuming the rest of your PC is high end as well).
Both companies support their products with regular updates, and stability is good on both sides.
Of the latest cards, I do believe that NVidia has a slight advantage. But AMD cards do tend to be less expensive.
Check out this website. It will deffinatly help you get educated, and give you more facts rather then anecdotal stories which you might get on any forum.
PassMark Software - Video Card Benchmark Charts