I can really only give you a partial reply. With ILS, if flown by an autopilot, the aircraft will track the centreline (assuming everything works as advertised) and there is no capability for a curved approach. Also, my understanding is that the aid is only calibrated and checked within a very narrow approach fan. MLS, though, I think, gives the capability to track multiple defined curved approaches - how it does that, I can't answer.
Any avionics or navaid experts around today?