Edit: Some searching shows that the base part of Beryl uses pretty low-level OpenGL stuff that any remotely modern video card with Linux drivers will support (similar to the regular 2D UI that Vista supports). Some of the extra effects are done through OpenGL fragment shaders (analogous to DX8/DX9 pixel/vertex shaders) and will only work on newer cards that support those shader types. So if you want "all" of Beryl, you'll need somewhat newer hardware as well.
The water effects and motion blur is probably what they are talking about. Motion blur works, but it's deadly slow since it's software driven. Water effects don't work at all.
Everything else I've tried does fine though.
edit:
One of the nice thing about OpenGL is that it's designed for writing applications, not nessicarially performing hardware acceleration. Most cards only actually accelerate a portion of OpenGL, which is typically what you'd see in games and the proccessing intensive portions of it.
So for a fully opengl driven interface you actually don't even need hardware acceleration at all. (technically. Although it's not how it works right now with X) It can be all done through software rendering, however that will be slow unless you keep everythig to a minimum.
In otherwords to go from a OpenGL 1.1 video card to a OpenGL 2.0 video card all you need is a driver upgrade, not a hardware one. Of course hardware designed for OpenGL 2.0 is going to perform better.