I don't think you can manually set the EE to hibernate. Or at least, it's not an option when you hit the power button and it's hidden somewhere I can't be bothered to look. I just always close my EE, and when I open it up again, the e-ink side says it's hibernating, press menu to come out of hibernation.
One thing you'll probably notice with the EE, assuming the battery is still in good condition, is the EE has a much longer battery life. I would try looking around to see if you can find a spare battery, before they are no where to be found. With 2 batteries, it's almost impossible to run out of juice.
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