dependent on the latency of Apple &
Android queues
I don't think that's true. It's up to the app developer and the server side implementation how much time this takes. I get my email pushed to my phone before my browser client gets it. And not just gmail, my corporate e-mail as well.
As for your question, you should work with whatever works best. Or even better, you should give the user the option to use push notifications or to set the polling period.
