Almost zero.
Runkeeper makes use of the M7 right now - recording your walking passively, even when the app is not open (the M7 chip is tracking your steps anyway).
The reason you use more battery when you have the app open and actively track your runs is that the GPS chip is being used, which is quite thirsty on the battery.
Ah thank you! (And thank you to others who replied). The battery on these iPhones are really my only complaint about them now that they are coming out with larger sizes.
I will have to check out Runkeeper.