I have an AMD APU in the PC I am typing this on (CPU and GPU in one chip package). Before that I had always used NVidia graphics cards.
For my next PC I would definitely choose an AMD APU again. I have had zero problems with it in several years of use. It's fast, glitch-free, and reliable, as are the open-source drivers used with it by default (I'm using Ubuntu).
In contrast I always had some problems with NVidia graphics cards used with multiple Linux distros, especially when using the proprietary drivers.
Considering the AMP APU comes with CPU and GPU in the same chip package for considerably less money than I would have paid for a comparable CPU plus separate graphics card, it is pretty difficult to justify anything else for typical desktop applications.
I don't play video games so I can't speak to that field of use. I use mine for software development, full screen video playback, and web browsing. I have no complaints whatsoever about AMD APUs in my applications.