Tom - If you need data to be available offline without internet connectivity then you should you SQLITE database which comes as part of android/ios.
If your app saves the data on server which in turn is used by other portal or other devices (sharing) then consider storing data via web/server and mysql database.
So really it depends on the usage and sharing requirements. Storing data locally has much benefit because it is faster, no network required, data always available, and not using network also increases battery life..
