A larger comparison is in the works to pit Manjaro against Ubuntu, Fedora, openSUSE, and other popular Linux distributions. However, for the increasing curiosity about Manjaro, here's the benchmarks that are complete at the moment: Manjaro 0.8.5 vs. Ubuntu 13.04.
Benchmarking happened from a Lenovo ThinkPad W510 notebook with an Intel Core i7 720QM processor and NVIDIA Quadro FX 880M graphics. Here's how the software stacks compare:
The results in full are on OpenBenchmarking.org in 1304239-UT-1304238UT67.
The Nouveau graphics performance for the Lenovo notebook appeared slightly better with Ubuntu 13.04 over Manjaro Linux 0.8.5. Both releases are using the Linux 3.8 kernel with Mesa 9.1.1 while Ubuntu is using Unity/Compiz over Manjaro's Xfce desktop.
Ubuntu 13.04 ran slightly better with compilation times. Ubuntu 13.04 depends upon the GCC 4.7.3 compiler while the rolling-release nature of Arch Linux already has GCC 4.8.0.
GCC 4.8 is known to be better for C-Ray with Intel CPUs.
There's other performance differences too as a result of the brand new GNU Compiler Collection found in Manjaro / Arch.
Find more benchmarks on OpenBenchmarking.org. The full multi-way Linux distribution comparison will likely be published next week.