Remove deleted files on target not working

Yes, SyncBack Free has capabilities simlar to Rsync in only copying new/modified files and deleting removed files on target.  It does not have the same incremental file modification capability -- it will replace the whole file when it is changed (which may be all DeltaCopy does, too).  The paid versions offer some additional options, including versioning.

Of course, you could do something like that yourself with Robocopy, but this is so much easier.  It seems faster, too -- I think it retains some information about the source and/or destination files so it doesn't have to check each one every time.