So I have been struggling with this same battle since day one with this phone...so much so that I bought a Nexus 6P to replace it. While using the 6P, I totally reset the phone and watched it's battery usage after a fresh new phone reset. It sipped battery. I'm talking like 1% over 8-10 hours. There was no sim card in it, but it still had cellular for emergency calls.
So I decided to put my sim card in it yesterday for Christmas and see how it went. I have been off the charger for 19 hours and am at 51% battery. It has taken 50-60 photos and had 37 minutes of screen times. It certainly didn't follow my usual pattern of use, but even then I couldn't have lasted 19 hours and had any battery life left before I reset. It may be important to note that I am on AT&T
Things I have done:
Reset as totally new phone
Setup my Office 365 Account for Exchange
Setup Facebook
Setup Instagram
Setup Moments for Facebook
Setup/upgraded Photos from google and configured to backup my photos
Disabled all AT&T bloatware
Installed a nice little snow covered Samsung theme
Left it configured for HD Voice (even though I'm pretty sure I have never gotten that functionality with anyone)
GPS is configured for wifi, cell, GPS, but location tracking is turned off.
Things I have not done (on purpose)
Configured Google Now (scared it is one of the major culprits of my battery issues)
Allowed AT&T to backup/restore/sync my SMS/MMS messages
It appears that the biggest battery drain is every time I turn on the screen. Big dips in the battery meter at those points, but that is to be expected. What kind of screen on time is good for a phone like this? 4-5 hours?