I think it really depends on the phone. Some phones have power saving, only turn on wifi when you use the phone. Some phones have better battery life. Experiment it yourself would be the best.
It's true that turning on the phone consumes energy,but not that much. And even when you leave it on, not much energy is lost as the screen adjusts itself to standby on to save energy.
I am using an android handset.. Really it consumes very much of battery in fact when I am not using GPRS or wi-fi..