Mozilla Firefox 4.0 will feature GPU hardware acceleration using OpenGL (or Direct2D/Direct3D under Microsoft Windows) acceleration for WebGL content and even HTML5. This support is there for Windows and Mac OS X, but for Firefox 4.0 the Linux support has been disabled and WebGL is also blacklisted for most drivers. Why? It's the problematic GPU drivers, of course.
We tried enabling OpenGL on Linux, and discovered that most Linux drivers are so disastrously buggy (think "crash the X server at the drop of a hat, and paint incorrectly the rest of the time" buggy) that we had to disable it for now. Heck, we’re even disabling WebGL for most Linux drivers, last I checked.
If your drivers are decent (some of the closed-source ones can be, nouveau can be sometimes), you do get something akin to Direct2D on Linux through XRender, though. So while you don’t get compositing acceleration, you do get faster canvas drawing and the like. drawImage, for example, can be much faster on Linux than on Mac. But only if you manage to find a driver and X version that happens to not suck.
We do plan to put more work into the Linux end of this, look for workarounds for the various bugs, etc. But we could really use some help from Xorg and distros and the like here.
It's a sad situation, but hopefully by Firefox 4.1 or another point release the open-source Linux graphics drivers will be in a better state. To see what you're missing out on, below is a video from Mozilla demonstrating hardware acceleration in Firefox 4.