I have written on the merits of 64-bit vs 32-bit, or on the AMD Bulldozer CPU Architecture Overview. An article in ithare.com gave a very good overview about the relative performance of various CPU operations. Below is the graphic:
Also see the often quoted Agner Fog: Instruction Tables.
When the CPU is not properly cooled down, then the PC crashes, see below video.
The solution for this particular case: Upgrade the BIOS.
I was just asked this question and referred to Phoronix: Ubuntu 12.04 LTS: 32-bit vs. 64-bit Performance. Phoronix is this excellent web-site run by Michael Larabel.
Below is a chart from 2012. Not all charts look this astonishing!
There is a an INCITE program (HPC Call for Proposals), where one can apply for CPU/GPU intensive jobs, the link is INCITE.
From the FAQ: The INCITE program is open to US- and non-US-based researchers and research organizations needing large allocations of computer time, supporting resources, and data storage to pursue transformational advances in science and engineering.
The machines in question: Mira and Titan.
Since using Alpenfoehn Gotthard CPU cooling has improved and the whole PC is more silent. On an otherwise idle PC, just
xterm and Chrome running:
$ modprobe it87
avg-cpu: %user %nice %system %iowait %steal %idle
1.25 0.00 0.25 0.17 0.00 98.33