i've been trying to find a way for the health app to display calories burned like the actual Fitbit device does. Even after trying every free health app in the app store and giving it permission to read and write to it, I still can't get it to work. That's where Fitbit has Apple beat. It just tells you 4 things, steps taken, distance traveled, calories burned and time of day. One would think that the health app would just do that much all by itself.
MapMyWalk also tells you calories burned during your walk. The app is free. It also maps your route, gives distance and time and stats per mile.