First of all what is the procedure you are following the in migration! we have to know the procedure in order to tell you what to check!
But after all, check for the sizes before and after! and if you can ls -al | wc -l before and after would be another check! If those filesystems are database data files or some application rely on them then starting that database or application will let you feel more comfortable about the data you just copied! du and df on the filesystems would show you more details as well! There are many things you can do to check the filesystems.
Regards,
Khalid