Thomas - you've had a real flash of inspired genius with that suggestion about the Code Completion plug-in. Disabling it makes the problem go away on both machines.
Actually I'm well-known and hated for the fact of blaming code completion as the first thing whenever someuse says the word "crash". Unluckily, I'm correct with that guess 99% of the time, too.
I'm actually quite surprised that it took 5 pages for someone to mention the CC plugin; it has a long history of causing hard-to-pin-down crashes.
To narrow down the source of the crash, please try disabling all contrib plugins first, and if that does not help, disable the "core" plugins one by one (start with CodeCompletion).
Not quite 5 pages.
If I read that message correctly ("unexpected async reply"), it seems like the plugin calls GUI functions concurrently from several threads, which X doesn't like?
