..without creating a temporary file:
diff -y <(ls First_directory) <(ls Second_directory)
The -y is just to show a side-by-side comparison. Very handy! And the result?
[jorge@j-laptop temp]$ diff -y <(ls First_directory) <(ls Second_directory) common.txt common.txt first_file.txt | second_file.txt
Thanks to my colleague Ingvar for showing me this!