In your case I would cache both ID and Reference in your datastore, as ID can be used to de-duplicate responses from the web service, and References can be used to get additional details such as photos and the like. When IDs shift, you'll want to revisit the data and confirm whether the new place is the same as the old one by your business rules.
I need to point out that you can only cache data from the Places API for performance reasons, and you shouldn't be storing the data permanently, as per our Terms of Service.