Man, for every PC thread, we get the nVidia vs ATi wars. It's personal preference. Both card manufacturers are currently making roughly equivalent cards. The only thing I could add into this discussion is on the topic of GTX 580 vs the Radeon HD 6970, the 6970 gives you about 90% of the power (usually more) and it costs you $100 less, takes less power, and doesn't heat up as much.
For most reviews of equivalent cards from either manufacturer, I see results that are either mixed benefits from one game to the next, or incredibly minimal advantages going one side or the other.
With the amount of cash you have, you can build yourself one hell of a PC. Instead of going single card, consider getting dual GTX 570s or Radeon HD 6870s.