Honestly I have no idea about UA. As for EVA, yes I have never had a bad experience with luggage so far. I have interlined with them on to AC and AC to them as well. Separate tickets. That said I am a G with them and normally fly on business and always do ask at the gate just before they start boarding if my luggage is on board. By then they can check if my bag is inside a container or not? EVA also notifies on their app if your bags have been loaded or not. Loaded means if they are in a container ready to be loaded on the flight.