Good point by iLounge's Jesse Hollington, writing on Quora, about the difference between third-party battery cases and the way Apple's new battery case has been designed to recharge an iPhone (via Zac Cichy):
Notice the missing step? You're only recharging your iPhone battery once instead of twice. The fact that Apple's case doesn't have a switch means that you don't really have an option to turn it on when you need it or off when you don't — if your iPhone is inside the case, it's being powered by the case. If you do this at the beginning of the day, as soon as you disconnect from the charger, that means that the iPhone remains at 100% until the case battery is depleted, then the iPhone gets powered from its internal battery. The fact that the case is integrated into iOS to provide power status is an added bonus as you get a clearer view as to what your overall battery capacity is.
If you remember to have a fully charged iPhone before putting it into Apple's case, then it'll run off the case's battery instead of draining its own. Thus, if you always keep it on and charge both overnight, the iPhone will always start using the case's battery first in the morning. That's smart indeed – too bad I can't try it on the iPhone 6s Plus.