The battle between the two best Graphic cards manufacturers started a long time ago.Since the late 1990's Nvidia and Amd have been trying to outdo each other In the beginning we saw 3D cards like Nvidia's Riva 128 and. AMD's Rega 128 which the best were one could get those days. As time progressed Nvidia released the Geforce line of products while ATI launched the Radeon line.Since then many cards have been released with many different capabilities like SLI in case of Nvidia and CrossFireX in case of ATI, new versions of DirectX were made compatible. 
When it Comes to performance we cannot declare one single winner as they have their ups and downs.
When we tested different cards on Company of Heroes We saw that ATI Radeon X1900XT beat every other competitor.In other games like Call of Duty we saw Nvidia to be the clear winner.
So if you are planning to buy a new graphic card there is no company that makes the best, some games work better on ATI and some on Nvidia. But are smart enough to Overclock the GPU Clock go for ATI.
Nvidia Vs ATI