I don't think rclone can give you a comparison-list from a built-in command.
@ncw Or am I mistaken here?
What you can fairly easily do with a little scripting though is use
rclone ls (or lsl or lsf depending on what data you want in the list)
And then you can script a comparison between the two easily enough.
I would think that it would be much easier to just do a sync after you delete on one side though (ideally right after you copied in both directions to make sure all files are up to date on your end). A sync will mirror any changes, including moves and deletions to the other side and make an identical copy. That seems much more straight-forward to me.
You can certainly do this in a few ways depending on the setup. Many remotes can be specified to be read-only access. Mounts can be set to be read-only on that level for end-users. The sync command can also be modified with flags like --immutable or --max-delete 0
Perhaps you would want to enable --backup-dir to keep the previous versions of modified or deleted files in case anything goes wrong (or just generally needs to be recovered - as is often needed in work situations as people make mistakes).
Normally --backup-dir only keeps one previous revision of files, but you can see here an easy example (demonstrated in batch script) of how you can make a full dated revisions system if you need that extra layer of security and administrative flexibility:
Hope that gets you on the right track