I did extensive research on this about 2 years ago for Android. Holding long standing connections is much more efficient than using multiple HTTP requests, polling included.
The reason being mainly the session negotiation and teardown required for making multiple requests, and the fact that the antenna required a higher energy state for creating a new connection compared to keeping an existing connection open.
Re:Heroku WebSocket performance
by thatthatis on Monday October 28, 2013 @05:46PM
(#6630061)
Is it the same result using cellular vs. using wifi?
It'd be interesting to see the trade-offs between web sockets and persistent polling.