Phoronix published a review on the AMD Radeon: Windows 8.1 Catalyst vs. Linux Gallium3D vs. Linux Catalyst A quote from the article:

Our latest Windows vs. Linux benchmarks on Ubuntu 14.04 LTS are of three different AMD Radeon graphics cards from three different generations as we test the performance of Microsoft Windows 8.1 against Ubuntu 14.04 LTS, when using both the AMD Catalyst proprietary driver and the open-source R600/RadeonSI Gallium3D drivers.

Earlier this week I delivered updated Intel Haswell graphics benchmarks under Microsoft Windows 8.1 Pro x64 and Ubuntu 14.04 LTS x86_64 and now the tables have turned to the AMD Radeon graphics cards. For this article the Radeon HD 5830, Radeon HD 6870, and Radeon R9 270X graphics cards were tested as a diverse spectrum of GPUs supported by both the closed-source Catalyst drivers and the open-source Gallium3D drivers from AMD.

 AMD Radeon: Windows 8.1 Catalyst vs. Linux Gallium3D vs. Linux Catalyst @ Phoronix