If you've ever lurked Doom9, you'll realize that AMD/ATi cards are very narrow in the types of AVC files they will accelerate, when compared to nVidia. And this is on the well supported and well funded Windows side.
They might have some support in the drivers, but Linux video acceleration is a clusterfuck, some really convoluted setup that makes PulseAudio/ALSA look like a sane design.
In Windows, video players will simply drop to software decoding if it can hardware decode, but in Linux, the video players try to hardware decode anyways, resulting in garbled video.
My nicest card is AMD, but my ancient Pentium 4 with a NV 8400 can DxVA more files... and it needs to.