I believe I have solved the case! A search on the error message "counter constraints enabled...etc." in the guest screenshot was the clue.
I tried a RedHat-oriented search on this error, since the guest type came in as RedHat-64 and got this: https://bugzilla.redhat.com/show_bug.cgi?id=921724. I then saw in the guest boot windows that this was really a CentOS 6.6 guest and reoriented my search, and got this: http://www.gossamer-threads.com/lists/l ... el/1716237.
Both indicate the error appearing due to either an error in AMD family 15h "Bulldozer" processors, or Linux's possibly-too-firm method of interpreting the AMD processor info. (Or possibly running in a virtual machine - see note below.)
Your Mac runs an Intel I7 Sandybridge, and your monster erroring server runs AMD FX-8150 Bulldozer family 15h. So the Mac runs fine and the AMD server doesn't. QED.
Solution? Unknown. Hunt down that error more. See if Linux has made an update to the issue, upgrade the Mac-Intel-based guest, then copy the guest to the AMD-based server (see Moving a VM for a super easy transfer method).
(Note: the above links, and another that might have to do with the same error https://communities.vmware.com/thread/5 ... 0&tstart=0 do all seem to implicate running in a VM: Virtualbox, kvm, and VMware, as an error vector. So maybe the developers might want to hear about this on the Bugtracker even if the actual issue isn't specifically Virtualbox-caused.)