real time notifs, push vs pull for mobile

thinking bout building a real time notification system for a mobile app. we need to alert users to new messages and events instantly. the options seem to be using push notifications or having the mobile client poll a server endpoint periodically. push notifications feel more immediate but can be tricky with battery life and delivery guarantees. polling is simpler to implement on the client but can introduce latency and unnecessary server load. what are your experiences with each approach, and when do you prefer one over the other for mobile applications