Sure and some of the problems have subsequently been addressed on the desktop side of things but I'm unsure about mobile which I used. It was actually four generations worth of AMD hardware, so I was wrong when I said 3 earlier.
4870/5870/6990/7970 mobile xfire: All had problems with the system never waking from sleep and needing a hard reset. Crossfire support was especially laughable with games often stuttering, outright throwing the system into a BSOD, flickering in games like Borderlands 2 (when it was released). Other games like Skyrim also had serious graphical issues that took forever to address. AMD also failed to support their mobile hardware at all, the 7970m didn't have proper working crossfire drivers for over a month after the card was released.
Here's an example of the 7970m xfire system I had, you can imagine I wasn't happy having spent >$1200 on the GPUs to have crap driver support like this:
https://www.youtube.com/watch?v=EeLnTfZypKQ
Once I switched to NVIDIA it was rock solid and I didn't experience any problems. Wake from sleep worked, AAA titles had day 1 driver updates for the most part and they have had consistent performance throughout a wide range of games. I can't say I had anywhere near as good of an experience with AMD so I won't waste my time and money on them again. Certainly things may be a bit better on the desktop side of things compared to their abysmal mobile support but that was enough for me to give up on them.