It just randomly panics? Do you have any common hardware between the two machines (SCSI is often a culprit in OS X)? I looked at the panic logs (which are in rtf format, not plain text like the extension makes it seem), and I didn't seen anything particularly striking (the back trace didn't seem complete), so its hard for me to tell beyond that. Its interesting to note though that they are not panic'ing on the same methods.
Sorry I couldn't be much more help.
iMac 800 15", Mac OS X 10.3.2
Dell OptiPlex GX200, RedHat Linux (ugg) 9