The open-source driver support for the Radeon HD 7000 series is less stellar than previous generations of AMD GPUs backed by the mature "R600g" Gallium3D driver. It's been a year and a half since the "Southern Islands" launch but the driver was enabled as a new Gallium3D driver rather than extending R600g. This driver right now is much slower for OpenGL as results have shown, the open-source driver only supports OpenGL 2.1 (not GL 4.x as supported by the hardware or GL 3.1 as supported by R600g), and there's corruption issues for some games.
On the NVIDIA side, the reverse-engineered Nouveau driver is also in a less than desirable state for the GeForce 400/500 "Fermi" and GeForce 600/700 "Kepler" series. The Fermi/Kepler Nouveau support does at least include OpenGL 3.1, but the main performance-limiting factor is that re-clocking isn't supported so the graphics card is locked to running at its boot speeds rather than at the full speeds where they were designed to run.
With both the Southern Islands and Fermi/Kepler support being handicapped, how does the performance compare? Here's some benchmarks. Benchmarks were done of the AMD Radeon HD 7850, AMD Radeon HD 7950, NVIDIA GeForce GTX 460, NVIDIA GeForce GTX 550 Ti, and NVIDIA GeForce GTX 680. This comparison was limited to available hardware.
View the rest of these AMD Radeon vs. NVIDIA GeForce Linux OpenGL performance results in full at 1306290-SO-KEPLERSOU42. Also coming up on Phoronix in the coming days is a 15-way Intel/NVIDIA/AMD open-source GPU driver comparison from Fedora 19.