Red Hat Enterprise Linux 6.2 vs. Ubuntu 12.04 LTS
Kicking things off with C-Ray, on all three systems the multi-threaded ray-tracer was faster with Ubuntu 12.04 LTS than Red Hat Enterprise Linux 6.2. This is likely due to GCC 4.6 vs. GCC 4.4, but RHEL users can unofficially upgrade to GCC 4.6 if they wish.
The lightweight Smallpt path-tracer did not see much change between these two enterprise-class Linux distributions nor did LAME MP3 encoding.