Does anyone know what could cause this? I am guessing it's something to do with the differences in processor architecture, but I'm no expert.
Well I'm only guessing too, but it could be things like:
Different operating systems
Different versions / releases of Java
32 bit versus 64 bit issues, at the JVM or OS level.
Different JVM parameters; e.g. those that affect heap size.
Differences in paging disk speed / latency (if the application is paging).
Other stuff running on the machine (e.g. resource hogging AV software)
It could also be processor architecture related ... as you postulated ... though I'd put that well down the list of possible reasons.