That should work as long as you are in the directory with the files and execute
Code:
cat diff_output.txt | xargs cp -vt /path/to/<backup directory>
or preprocess the diff output to include the full path.
xargs will just append its input. If you say
Code:
cat diff_output.txt | xargs cp -vt <backup folder> <path/ to/ location/ of/ the/ extra/ files/>
and diff_output.txt contains the files 'foo' and 'bar' then cp will get
Code:
cp -vt <backup folder> <path/ to/ location/ of/ the/ extra/ files/> foo bar
You can't copy a directory onto a directory that way and foo and bar still won't exist.