When I started reading through this I initially assumed that this was the usual teenage-esque defense of 'whatever I happened to have purchased is obviously better than the other thing you bought.' Having seen the cards that people have had and decried as crap or praised as great, it's obviously older people. Very disappointing!
I had a Matrox Millenium. It lasted less than a year and stopped working. All Matrox cards are crap. What? That was just my own experience and some people may have got a decade out of them? No way! Whaddya mean they don't make them anymore...
The only thing this conversation proves is that quality control is really, really important in the electronics industry. Once you've sold someone a product that fails prematurely or doesn't live up to expectations, even though tens of thousands of others work just fine for a long, long time, you've lost them as a customer. And, with the reach of the internet, they can tell everyone that the 'Nvidia/AMD/Ati* xxxx' is utter rubbish and doesn't work properly. Oh, and those crappy Matrox cards. That will be right above the post that says how brilliant the 'Nvidia/AMD/Ati* xxxx' is and anyone who says otherwise is obviously having sexual relationships with someone in their family. Matrox cards will never be good though, because they're not made anymore and I bought a bad one.
* Delete according to how old you are!
It's been said already but worth repeating - these two companies leap-frog each other constantly but sometimes it's not clear where. AMD have pretty much bowed out of the single card top-end race but you can't go wrong with one of their mid-range offerings. Nvidia peddle over-priced coin-miners/folding machines/computational devices as well as the single best bang-for-buck card on the market - the 970. Who cares if you're actually missing 500Mb of VRAM - I build properly demanding games for a living and the news barely caught my attention.
When you're dealing with games shipped by the big publishers, who write their own engines, then some of what has been written above does come into play. Optimisation, bribes - oops, I mean technical advice and development assistance funding - all of that has been, can, and will be an issue.
For everything else that is built on a non-proprietary engine, it doesn't matter. Pick your budget, do a quick google search and you will find the best hardware for your price-point in minutes. Sometimes the winner is AMD, sometimes it's Nvidia. If you find they are equally good (the horror!), simply pick AMD if you live in a colder climate, preferably with cheap electricity, and Nvidia if you live in a warmer climate.**
**That previous sentence may or may not apply depending on which range you pick.
See how silly it all is?
The trick, of course, is to do none of the above. Don't buy a current generation card. Do what we do here in the studio which is to pick hardware we think we will be mid-range in 18 months and buy last-gen from suppliers keen to get rid of old stock. My dev rig has two 780Tis in SLI and cost next to nothing because everyone wants the latest and greatest. I can work and test an SLI setup, disable one if the drivers throw a hissy-fit and it has yet to encounter anything it can't handle at max-settings at 1440p. 4k is here, but it's not the modal setup.
On a different note, I've just bought a Volvo V70.
Feel free to post 'shut up dumbass, everyone knows Lamborghinis are faster like what I have and my super-model girlfriend's BMW is so much cooler. Stupid fag Volvo drivers.'