In my experience the AMD drivers&software have been more stable. Probably I just have bad luck, but just today I got a pop-up from the Nvidia Experience that there's an update. Clicked it and got 'cannot connect to Nvidia servers' or something similar. The last driver update failed to update one of the components. And the display adapter has crashed once (managed to recover though).
I'm currently using GTX 670 (got the Windforce model and it is really quiet) and I'm reasonably happy with it, but I had none of the update problems with my previous HD6850. Of course, my thinking may be coloured by the horrible nvidia chipset I once had. Or the lack of support for my previous laptop gpu. Compared to those, my current GPU problems are minimal at worst.