It could be due to comparing "Size on disk" instead of filesize. The filesize is the exact number of bytes needed whereas size on disk is how much space of a disk drive is required. The descrepancy arrises when you have two disk drives with different sector sizes.
(example: a 513 byte file on a disk with a 512 byte sector would require two sectors and take up 1024 bytes on disk. That same file on a 4096 byte sector would take up the entire 4096 bytes on disk. It doesn't seem like much difference but if you have thousands of files, they add up.)
Use the Get Info command in the Finder for each copy of the library and you'll see the size of the library and also the size on disk.
If you're looking at the size in a Finder window I believe it is showing "size on disk".
This is only a theory. See if it helps.
does your external drive have the same file system? Is it formatted "MacOS X Extended (Journaled)"?
If not, I'd reformat the drive, before you copy the the library there. An Aperture library will not work properly on a drive not formatted for mac.
You'll see the formatting in the Info panel of the drive when you select the drive in the Finder and use the command "File > Get Info".