I would first check carefully that all the files were actually copied. Often the simplest explanation is the correct one, in this case that some files weren't copied for some reason.

That said, I have seen something similar once, and the reason was something called sparse files. We had some database backup files on a FAT32 partition (don't ask why), and we copied them to an ext4 partition. We noticed that the copied files occupied about 1/4 less space than they did on FAT32. Turned out that the backup files contained large amounts of "empty" space (zeros bacially) and because FAT file systems don't support sparse files, that empty space occupied physical disk space on FAT32. On ext4 however, those empty parts didn't consume any physical disk space and thus the total disk usage was way lower.

Does your data include disk images for example? If so, this could be the reason.