The open source AMD driver has improved a lot over the past couple of years, it's really pretty good. "Pretty good" is unfortunately not good enough for really 3D intensive tasks like newer games, etc. Good enough for the vast majority of desktop tasks though including hardware-accelerated video rendering etc.

The closed AMD driver is pathetically bad. Neither multi-monitor mode works for me in Gnome3, due to from what I gather is AMD not keeping up well with architecture changes. AMD is also dropping support for their oldest architecture in their next driver release, leaving a ton of cards - some still being sold today - with nothing but the open source driver anyway.

My next video card is going to be an Nvidia for sure. Whatever Nvidia's faults, their proprietary linux support cannot possibly be as poor as AMD's.