I go for whatever is the best at the time.
Almost all of my GPU's up to my latest one have been nVidia.
I chose nVidia for a few reasons, mainly driver support for linux.
I guess I had gone for nVidia previously as their build quality, support and drivers was superior to ATi.
On my X1900XT I decided to go ATI as there were problems with the nVidia cards and also the X1900XT seemed to perform better when using Anti-Aliasing etc. Also the linux ATi drivers seemed to have improved a lot.
I think a nvidia card with the same performance was also a lot more expensive at the time.
I'm not sure about picture quality. I've seen comparisons, but I'm not sure they were fair tests.