Database Synchronization Algorithm Advice
I have not been involved in this directly myself, but I have been around when people were working on this sort of thing. Their design was driven not by algorithm analysis or a search for performance, but by hours spent talking to representatives of the end users about what to do when conflicting update requests were received. You might want to work through some use cases with users. It is even possible that users will want different sorts of conflict resolution for different sorts of data in different places.
All the designs here save bandwidth by propagating changes. If something ever causes one side to stop being an exact copy of the other, this inconsistency can persist indefinitely. You could at least detect such a problem by exchanging checksums (SHA-2 or SHA-3 if you are worried enough). One idea is to ask the recipient system for a checksum and then select an package of updates based on that checksum.