I Have been running through full battery for iPhone 6+ in 2-4 hours! Made a GB appt but kept playinv for an answer and here's what I got that fixed it for now:
for the shutting off at 18-19#% problem I did what Lawrence recommended & it worked so far. After it shut off, I plugged in for two min, then took the cable out first, then force rebooted, and when it came back on there was a sudden jump from 20% to 4% to 1% and then I put a movie on silent and ran down that last power which took 2 hours!!! ( so it had more than 1% obviously) and then I plugged it into it wall charger and left it for 4.5 hours.
To solve the rapid drain problem I took over all the setting manually. I turned off most background refresh, took off auto bright, took off everything I could find that seemed optional just to find the issue(there's alot of manual settings, if you don't know go have a deep look into the settings app & see how much you can turn off!!) After two days it was iCloud Drive that was found to be the cause. When I turned off that, the problem went away. Bottom line: the battery status is not the whole story, start turning things off to find out what is causing it!!! It took two days because to isolate variables you can't do everything at once! Ok? Do it piece by piece to see what happens...
OTherwise do do a restore as new or go get a new battery. Neither of those are the end of the world.