It takes a few days for iOS to settle down with all its background functions. Did you calibrate the battery? (run it down until it switches off then charge to 100% in one sitting). It's not so much the battery as it is iOS, it needs to be taught where 0% specifically is by draining until it can't drain anymore.
Took a few days, but my iPhone 6 is chugging along nicely now. My 5s used to be dead by 6pm after starting at 8am, while my 6 survives the work day easily.
Take note though, poor signal obliterates iPhone battery. You spend a few hours going in and out of shops in the city centre with the signal jumping between no service and service, and you won't get very far at all.