In my opinion the best Graphics Card company is ATI. Nvidia does keep up to their main keypoint to their graphics cards which is speed but whenever I see Nvidia the company seems to be bragging about their cards more than ATI. ATI though, besides having incredible graphics which in my view are higher than Nvidia, are not picked by too many game companies and they don't appear to brag too often.
I've always been an nVidia fanboi. I remember I used to have a Radeon 9200, and then got it switched for nVidia's closest equivalent, the FX5200. I noticed a lot of better things in the nVidia card, and I've used them ever since. I now have a 6600GT, and it works beautifully.
No debates of this kind are allowed, as they usually turn into a fanboi bash-fest. Read the stickies. ;)