I originally assumed both would be x64, but I'm not sure if Chromium installed through Ubuntu's software center is 32 or 64 bit. The shell was 64 for sure. Thanks for the additional parameter to check.
We picked these versions because that is what installed on a regular user machine, but on my Windows box it has 3.12.19.15, so maybe a newer version isn't such a bad test. And as you say nobody there likely cares about the difference in this version.
The subtests that differ don't follow me across different CPUs (Ivy Bridge vs. Llano vs. ...), but there often seem to be a couple that are faster in the browser. Originally we found this on an AMD Bobcat (E 350) CPU, and the two tests were ai-astar and audio-oscillator. Ai-astar was about 25% faster and audio-oscillator I think was even higher. I don't have the machines or data in front of me today to say more conclusively, but maybe this can spark something. I think audio-oscillator might have been common to the lists.