Both. Why not save power by turning off the router while shrinking the amount of time there is to break into my Wi-Fi network? I can't see a reason to leave my network on while I'm out of my house. I don't need it and as far as I can tell, my neighbors don't either.
That said if someone needed to use Wi-Fi, I'd be happy to open a guest network for them (I think my router can do that but I haven't checked).
I can understand power concerns (though I think home routers use very little KWH), but frankly shutting your router off every day to prevent intrusions is bordering on tinfoil hat-level of concern.
If you shut off WPS on your router and use WPA2-CCMP with a good passphrase, there is really no concern of someone getting into your wireless network.
That said if someone needed to use Wi-Fi, I'd be happy to open a guest network for them (I think my router can do that but I haven't checked).