You said Linux, so you luck out (at least it should be available, not sure when it was added):
diff --brief --recursive dir1/ dir2/ # GNU long options
diff -qr dir1/ dir2/ # common short options
Should do what you need.
If you also want to see differences for files that may not exist in either directory:
diff --brief --recursive --new-file dir1/ dir2/ # GNU long options
diff -qrN dir1/ dir2/ # common short options