Power saver or shutdown - which conserves charge better? If I want to leave my phone undisturbed for a few hours but want to conserve as much charge as possible, should I leave it shut down or in Android's power saver mode.

Also say I want to check the time every half an hour, would it be better to leave it in power saver, or shut down, and start the device every time I want to see the time (or make a short call at the most)?

P.S. I'm using Jellybean, but answers for other OSs can also be posted for reference.
Power save conserves better battery since rebooting or switching the device on typically drops battery charge by a minimum of 1 to 1.5 % , as you can test yourself. This is  hardware related and pretty much independent of OS version

Restarting the device twice an hour (to check time), puts the loss in the range of 2 to 3 % , if not more

Device running in power save doesn't consume that much power as you can verify yourself using battery monitoring apps on play store. In addition, you can reduce power drain by adopting measures mentioned here What is the best state to leave an Android device in?