I'm not impressed with my battery life either. Not very different from my Note 3's usage, and I haven't bothered to troubleshoot.
One thing I noticed, however, is the rather warm screen after I turn it on for a few seconds to check my messages and turn it off again. I usually place my phone in my front pocket when I drive, with the screen against my body instead of facing outwards. The screen is distinctly warm, to almost hot, for a few minutes before cooling off. I'm not sure if this is due to the glass protector I have on, or what. My Note 3 was in an S-View cover previously, so that may have prevented me from feeling the heat then. This is not a major problem, but I would like to know if anyone else is suffering from fried nipples like myself.