Benchmarking Ubuntu 8.04.4 LTS To Ubuntu 13.04
A separate Phoronix article is looking at the graphics performance specifically, but as you can see, the open-source Radeon graphics driver has matured a long way with succeeding Ubuntu releases. Between Ubuntu 10.04.4 LTS and Ubuntu 13.04, the open-source R600 Gallium3D performance has more than doubled. How though does this compare to the proprietary graphics driver? A future Phoronix article will specifically answer that question.
With succeeding Ubuntu Linux releases, many computational workloads are also faster thanks to optimization/performance improvements within GCC, the Linux kernel, and other areas of the key system stack. Between Ubuntu 12.04.1 LTS and Ubuntu 13.04 is in fact the biggest performance improvement for the multi-threaded C-Ray ray-tracer on this aging AMD Phenom system due to GCC 4.7 improvements.
Ubuntu Linux though isn't regression free and some workloads due experience slowdowns from time-to-time.