I can't speak for the state of AMD's drivers for your particular system and games, because there's no such thing as bug free software, but I can speak about how seriously the AMD driver team took any report or complaint about a bug, broken functionalty, and stability. It's AMD's traditional Achilles' heel, and the SW dev teams work tirelessly to make sure they don't regress backwards and get that reputation again.
That's not to say bugs and problems won't happen on AMD, but if you report a bug and provide repro steps, the chances are high that it'll get addressed in the next possible driver release. There's latency for new features being accepted into the GPU driver, but very little latency for fixes. That's especially true for anything popular that affects a large swathe of the customer base, but I've seen bugs that affect a single user get fixed in a single release cycle.
It's a very high quality driver today as a result, especially in certain subsystems (any of the client API drivers built on PAL in particular). If you have an issue and aren't sure how to report it, I can help.