nvidia drivers tend to be more stable for professional use. while this does not mean they are never without problems generally this is true. nvidia is typically suggested for professional applications like photoshop, cad and other such programs (not sure about game developing). while you can certainly use amd cards for many things (amd also makes professional series cards) nvidia is typically the go-to solution when using regular gaming cards for professional tasks.
stronger? depends. cards like the gtx970 are really powerful though the slightly cheaper r9-290x is in close competition and in a few limited cases may exceed the performance. the 290x draws alot of power and runs as hot as an oven with a rather low thermal threshold. it also generally loses in most things to the gtx970 so the 970 would be much better overall. as for other price-ranges of cards it depends on the card and what individual prices are. amd cards typically do pack alot of value but run hot. nvidia normally costs more but runs cooler. to say which is stronger depends on the money you want to spend on a card.
from the maya forums:
nvidia cards are stable with maya and zbrush and always have been. amd cards tend to be less stable though a few users seem to have no issues. read more here
http://simplymaya.com/forum/showthread.php?t=38935 . now quadro/firepro cards will do it best (professional cards) but a normal gaming card will work too if that fits your other needs better.
gaming cards render games better (focus on speed over precision rendering without errors). professional cards render other things better (less time since they focus on precision so do not have to reprocess information). the drivers used are also somewhat different and focus on professional tasks to optimize them.