A long time ago, before I tried incremental and differential backups, I tried to tar/gzip several similar large (1 GB) directories, but they did not compress any better than tarring and gzipping each directory individually. My guess why it didn't work is this:
tar was likely not going to put duplicate files next to each other
because files were far away, they would be in separate gzip DEFLATE blocks and so not be compressed together (I've also asked how far)
Is this reasoning correct?