Transferring data to a new external hard drive without breaking links
This might be due to the file system’s allocation size. 

To check, use Get Info to get the space on disk for a tiny file on both disks. 

For a more definitive answer, try this command in Terminal on each disk:

stat -f %k .


If the large disk uses a larger size, your small files will take extra space. That can be resolved, but it might not be worth the work.