Their drivers aren't crap, but they aren't up to nVidia's standards. I've a 7970M in my laptop, which I got when it was a brand new chip, and it has been a trial. So there are two big issues it has had, only which could be relevant to the PS4:
1) Issues with Enduro, that's AMD's hybrid GPU switching. The laptop can use the integrated Intel 4000 graphics for easy stuff and fire up the 7970M for hard stuff. Well until fairly recently, that didn't work that well. The 7970M didn't operate at full capacity, something with the drivers was inefficient. You could see it on other laptops which has a mux to allow you to switch off the iGPU. With just the 7970M they ran much faster. AMD finally got it (mostly) fixed, but it took for damn well ever. Also when it first came out, the interface for choosing GPUs was really clunky.
2) OpenGL issues. AMD has sucked at the OpenGL for as long as I can remember, and it never seems to get better. They SUPPORT it, but it doesn't work well. On nVidia, GL and DX run equally fast. They are both first-class APIs and there really is no speed or capability difference between them. On AMD, not so much. Recently the issues I've seen were with Brink and HFSS. Brink was a shit (man it was a waste of money) game that used iD Tech 4. As such, OpenGL. On my AMD GPU, it never ran well despite being WAY passed the spec needed. Tried it on a lesser spec nVidia system, flawless. Said problems were all over the forums. With HFSS we set up a desktop at work with a cheap AMD chip, a 7570 or something like that, just for basic graphics (it was server class hardware, so no good iGPU). The user reported HFSS worked over RDP, but not local and sure enough, that was the case. So it occurred to me: HFSS will use OpenGL to accelerate its interface. Out came the AMD card, in went a cheap nVidia GT 210, and HFSS worked fine.
Now of those, the OpenGL problem could be problematic to the PS4, since that's what it uses. Maybe they won't have a problem since this is ONLY a GL driver and they've had time and all that, but I worry. The PS4 may lose its, on paper, graphics advantage due to driver issues. It would suck for Sony if their console which has more graphics units and more memory bandwidth had lesser GPU capabilities because AMD can't work out a good GL driver.
At any rate the overall situation is AMD still has problems nVidia drivers don't. I really like AMD's hardware, it is often faster and is nearly always a good price, but I get continually bit with driver issues. Not something huge like "The system blue screens and won't run," but things that are very real and very annoying. Hence I have nVidia in my desktop and I've seriously considered replacing the card in my laptop (it is a Clevo laptop and the card is field replaceable). They aren't perfect, but I find them WAY less problematic.
And don't even get me started on Linux drivers. There is NO comparison there. nVidia binary drivers is lightyears ahead of anyone else.