How to compare (diff) files completeness on two computers?

[joe at actionline.com]

Is there some efficient way to compare the completeness of all the
directories and files on two different computers?

I used rsync to upload all the files from one computer to another (or
thought that I had done so), but I have since discovered that some of the
files on the source computer are missing on the target computer.

Manually searching each directory and sub-directory is obviously very
tedious, so I wondered if there was something like 'diff' that could be
used globally.