I had to check the file changes between two Backintime snapshots recently. You can always use rsync for that, but there is a more straightforward way by using diff.
$ diff -qr directoyr-1/ directory-2/
-q will display only the files that differ.
-r will make the comparison recursive.
There is a GUI application called Meld that provides similar functionality, but the diff approach will work anywhere and requires memorising less flags than rsync.