If you are not in an LTE coverage area. There should be a programming menu that allows the LTE to be disabled and just use 3g and 1X. Saves on battery as the unit is always looking for a LTE signal.
(Verizon) Samsung Galaxy S4 - Rooted - VRUAMI1 (STOCK) | (Verizon) Casio (GzOne) Commando 4G - Rooted - C811M020 (STOCK)
I also think there may be something related to being on the edge of a 4G area, and the phone constantly swapping between 3G and 4G radios. I look forward to apps to disable one or the other as needed.
All that said, I am getting as much as I'd expect given what is in this phone. It's 3pm here, I unplugged almost 9 hours ago and have used it heavily, and I'm still hovering just under 70%.
I have turned off all haptic feedback, keep the screen brightness down (heck, even at 0% I still think it's visible outdoors), and have manually set all my sync timings.
My screen usage shows 80% and I have it down to 13% brightness. I turned off all sync except for mail(who actually wants stock updates and a lame weather sync?). I killed the battery in 4 hours with mobile hotspot as a test to see how it handled without power. I considered that pretty good since I have been surfing sites on my laptop and checking emails on the phone as well.
I'm right in the middle of my 4G area.
You have to realize a battery will not perform optimally until it has had 2 or 3 recharges. The first charge and decharge will be much worse. If it still shows those results after the battery broken, there is a problem.