That's the problem though. ATIs performance last I checked was horrible. And since AMD opened up their GPU documentation their non-free driver got to the point were it's not worth trying.

ATI/AMD performance compared to intel graphics better than to nvidia graphics.

I'm a Linux user since more than 15 years and have been using nvidia most of the time but went through matrox, s3, intel, via, and ati, too. I really wanted to switch to a more free option several times and I did try. It just was never worth the performance loss.

So what from a user perspective are the problems with nvidia graphics day to day? Of course the drivers are non-free, unless you use nouveau but then you are better off with AMD. So let's say you are fine with running nvidias non-free drivers - what problems will arise?

There is no kms and it doesn't work to use framebuffer drivers together with the nvidia driver. So no high resolution text mode.
Switching between X and Text virtual consoles is flakey. Sometimes you loose text virtual console visibility. On a Desktop however 99.9% of the time you stay in X. On very rare occasions This switching left me with no graphics whatsoever and only a reboot helped.
RANDR support is there. Since this happened multi-monitor support is decent using the distributions own configuration tools. no need to change your Xorg.conf file.

Sometimes after a kernel update or a graphics driver update there is a mismatch of driver versions and X won't start. DKMS and other infrastructure by the distributions mostly takes care of that.

On the other hand when it works, and it usually does, the experience is unmatched. You get reliable and fast graphics with opengl just working. There are apis and api support for video playback acceleration and cuda. And there is infrastructure to actually use it.

In my opinion not using nvidia graphics for a Linux desktop is a very bad idea. Unless you value the freedom of your systems software over it working.

Edit: I did some more reading about the non-free amd/ati drivers. Apparantly the situation improved a lot. So non-free AMD/ATI can now actually be compared to non-free NVIDIA. That being said I'd have to try myself to actually see wether installing the ATI drivers has become something that can be done without hours of cursing nowadays. The ratio of nvidia/fglrx problems I've seen strongly suggests prefering nvidia.

Ew! Intel GRAPHICS CARDS would never rank higher than last on my list. >_<
I love Intel but their graphics cards are not very good.