If the hard drive can be removed from the USB interface and onto SATA/ATA, I would install it in the destination computer. You'll get much faster transfer speeds, as others have noted. For copying, assuming youryou're on windowsWindows, I would do a simple ROBOCOPY. It's about as fast as you can really hope for, though there are other alternatives.
ROBOCOPY /E /B /MT 'source' 'destination'
I'd try to avoid compressing all these files though, there is a good chance the time to compress and move would exceed simply moving the files.
*Added the /MT option for robocopy. It can greatly speed up transfers when youryou're in a multi-thread environment.