A contactor is just a high current relay.
A shunt trip is an accessory that is typically installed on a breaker that is designed to accept it.
They do different things, and are applied in different ways. As an example, a motor starter which has over-current protection can often times use BOTH in the same system for different reasons.
Regardless of what you choose to use, both will require some type of control system because by themselves, don't do anything. Often times, the Bartium system is doing the control. Your Batrium should be powered by your Powerwall and should not loose power.
If a contactor has the ability to be wired "fail open" or "fail closed", you could get creative with what might happen during a loss of power event.