There is much better performance of AMD cards from both the open source driver and the Radeon driver from ATI since 12.04. Upgrade to the latest version of Ubuntu 15.10 or 16.04.
For future travellers there are two issues with video playing:
- Playback refresh, the tearing mentioned above is caused by the frame rate and the playback rate being different and the display method refreshing scan lines instead of whole frames as a cached block.
This issue can be solved by using a video driver that takes advantage of the graphics drivers different ways of caching content and quickly displaying it all in one go. Effectively syncing each frame to the refresh of the screen.
- Decoding time, video is almost always encoded in a file which needs to be unpacked in real time. This puts a large demand on the processor to run very complex maths just at the moment you need that particular frame. If your processor is slow, old or broken (or in power saving mode) you may notice performance issues such as stuttering and frame rate reduction.
This issue is harder to solve; you could always buy a new computer of course. But the main way is to offload the decoding from the inefficient CPU to a dedicated video decoding chip that a lot of modern video cards have. You need three things for this to work. a. that the driver supports the chip, b. that the video program supports hardware acceleration c. that the video file is of a format supported by the chip.
So should the stars align for you, it is possible to get better video playback, even with an older machine.