Power saver or shutdown - which conserves charge better?
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?