Verified on three machines with identical hardware.
AMD doesn't have decent drivers even for Windows. (By decent, I mean less than 1 graphics-related crash on average per year.)
Counter anecdote mode: engage!
As an owner of many Nvidia cards, I find they crash infrequently, and when they do it's because:
* I was running Windows 8 Preview and pre-release Nvidia drivers
* There was some sort of hardware problem with my systems
I have used four ATI/AMD graphics cards over the years. Not all of them were negative experiences, but none of them were relatively more positive than using Nvidia hardware.
Before that, I had an ATI HD 5870 for over a year. I had about 3 crashes on the desktop, some that lost me work. The anger from losing work is what I remember most strongly, and made me vow not to buy ATI next time.
Before that, an 8800 GTX. I had 0 crashes from the desktop over several years.
I was running Nouveau drivers on the 670 for no more than 60 seconds before it crashed.
I think it's more about resources -- NVIDIA and ATI have lots of money that they put into driver improvements and maintenance, and the radeon and nouveau maintainers primarily have free time after work, occasionally with one or two full-time contributors. If we are serious about open-source driver platforms, we need to figure out how to allocate comparable resources. Some easily accessible tutorials on 3D driver development would probably be helpful.
Neither company ever plans to see an open-source driver rival their proprietary within a few years of a card's release, despite their "commitments" and "assistance". ATI's officially stated strategy is that they provide documentation so that the OSS drivers can provide basic compatibility and functionality, and that their proprietary driver should be used by anyone who has actual performance needs. They're basically offloading the onerous maintenance of previous generation hardware on the community.
The point is that nvidia is not especially bad. They've graciously given us the only consistently decent video driver on Linux for 10+ years now, despite its closed nature. Let's try not to be too hard on them.
I don't want to give the impression that I'm ungrateful for the help that ATI offered the implementers of drivers for its cards, but I think when we take all the facts in balance it comes out in a wash or even with nvidia slightly ahead: nvidia has been consistently producing a high-quality, near-performance-parity driver for Linux for a very, very long time now, and it's almost always compatible with new kernel and Xorg versions prior to their release. ATI has given docs for basic functionality in the free drivers, but they've utterly failed to produce good, performant drivers for Linux machines, closed or free, and in fact they are now on the verge of being two Xorg releases behind.
nvidia may not have "committed to help the open-source community" until recently, but they've done a great service for Linux by being the only vendor to provide consistent, solid, high-performance drivers for Xorg and the kernel. Intel has shaped up recently and gone full-bore OSS, but nvidia has a much longer track record of good [closed] *nix support.
i can tell you, however, that the specialist cards typically are only in super-computers. consumer GPUs are typically faster, and significantly cheaper than their HPC counterparts.