So, I installed Linux Mint Debian Edition on my laptop and my desktop last night. I then installed Firefox Nightly on both of them and went to http://demos.hacks.mozilla.org/openweb/HWACCEL/ to test performance and see if hardware acceleration was working.
My laptop has an Nvidia Quadro FX 570M with the latest binary drivers downloaded from Nvidia's website. The card is like 4 years old and was never a power house, and yet it was able to get 60+ FPS in the browser test, proving that hardware acceleration was working correctly.
Next I tried it on my desktop which has an ATI HD5850 and I installed the fglrx-driver package with apt-get. Compiz and other OpenGL application seem to be working fine, and WebGL seems to get good performance in the browser, but when I run the hardware acceleration benchmark, I get 18FPS.
My desktop's graphics card is easily 8x more powerful than my laptop, so obviously something isn't right.