I'll let you decide on which is best by letting you use the SEARCH function of this forum, as well as Google.
I'll help to sum it up a bit though
ATi and Nvidia are just two different video card chipset manufacturers. For the most part, other companies take their chipset, modify it, and sell it as their own product. For example, eVGA might take a 7600GT chipset from Nvidia, and overclock it, and put a big heatsink on it.
The same applies to ATi. However, ATi will often make their own cards from their own chipsets as well.
Which is best? Well, it depends on who you ask, really. Most people are favorable to one or the other, most times. When I am looking for a video card, and trying to figure out which is 'best' I usually have one window open looking at benchmarks, and another open looking at prices.
I am favorable to Tom's Hardware's Interactive VGA charts:
It offers an easy way to compare video cards.