Should i turn my Iphone 5s OFF or leave it on Airplane mode during the night?

Will either make a difference on the battery life?

Turning it off will use no power so will save all the power
airplane mode does save a lot of battery since it disables its Wi-Fi, Bluetooth and signal receptors which saves power but there's still some power being used to keep the device on such as sound, light etc

Honestly, I think you should only turn on Airplane Mode when you're actually on an airplane. The way to conserve battery life at night with an iPhone is to turn on the "Do Not Disturb" feature and set a time limit on it. You can set it (for example) to turn on at 10pm and not turn off until 8 or 9am in the next morning. This will minimize all running apps in the background AND turn off Wi-Fi so that your phone will only use Wi-Fi if you pick it up during this time. Also remember to erase all the recently used apps by double tapping the home button and swiping everything up until all you have left is the homescreen. Turn the phone on Mute also. This will also help you sleep if you occasionally have a random call in the middle of the night or even a text. You do also have the option of turning the phone off but if you're like the rest of America, you never do that. It takes far more battery power just to power the device on and shut it down than it does to just leave it on all night.