Video fails to play in QT browser plugin. Encoding problem?
Well the program that encoded the file that works was Apple QuickTime so not much of a suprise that it's working. QuickTime can be a little picky when it comes to mpeg4/h264 encoded files.
I looked at the files and possible factors are the encoding profile and maybe the GOP setting. Basline Profile Level 3.0 for the broken one and Main Profile Level 3.1 for the working one. GOP setting of M=1, N=120 and N=1 for the broken one. Could be that the Quicktime Plugin wasn't made to handle that.

An easy fix would be to re-encode it with Quicktime Pro or the free and open source tool Handbrake http://handbrake.fr/ and choose one of the Mobile presets for apple devices or simply the "Normal" preset.