Recently, I made a backup copy of a folder that I copied over several devices. In the end, I wanted to make sure the various copies did not alter any of the files. Here's how to proceed:
cd <ORIGINAL FOLDER>
find . -type f | sort | > /tmp/original.files
cd <BACKUP FOLDER>
find . -type f | sort | > /tmp/backup.files
# You may not have copied all the files, so let's only keep the common ones
comm -12 /tmp/original.files /tmp/backup.files > /tmp/common.files
cd <ORIGINAL FOLDER>
cat /tmp/common.files | xargs -d'\n' md5sum > /tmp/original.md5sum
# -d'\n' so that filenames with space characters are handled
cd <BACKUP FOLDER>
md5sum --check /tmp/original.md5sum # Shows OK or FAILED for each file
Hope that helps.