As per my opinion -it totally depends on use-case, where you want to manage the control over data, like from client/device end or server end/central database.
But i would like to add one thing here , the device is powerful resource, use it to Synchronize the data from central to local database and send/delete/update accordingly,
Reason being on server end, one/developer already has to manage the incoming request, querying the database and business logic, why not use the Client's computing power to do some mundane stuff, that's what i think is appropriate.
Others opinion may differ based on scenarios and perspective.