I have a Thinkpad x120e with AMD Radeon HD 6300 graphics. Under Windows 7, the machine can play full screen 1080p videos on YouTube well with some occasional hiccups, and 720p videos with no problem at all. However, when it plays same videos under Ubuntu 11.04, it suffers from low fps (10 stage fps, ~5 video fps according to video info.) Same thing happens with local video files. Apparently the problem is that hardware acceleration is not working even though hardware acceleration box in flash settings is checked. I am using AMD's proprietary FGLRX video driver. It feels like Ubuntu is not utilising graphics adapter at all. Any ideas?
It may be possible that you are not using a vaapi compatible media player like mplayer-vaapi?
You may find it as libva, xvba-video or vaapi. Without this Video Acceleration addition the media player don't use your GFX card as you expect.
I can not give you a more specific answer since I'm not using Ubuntu but ARCH Linux. But I suggest you to read this wiki page. It may apply to your situation.