Battery drain after the Kitkat update has been a problem for some folks across a range of devices.
I'm a Moto X user, and this has been discussed at length in forums for that phone, though I have not seen it myself. Android OS seems to be one source of activity often cited as using battery power. I don't know how well any of these would translate to your case with the S4 because of the different UIs, but some questions might be useful to know:
1) do you routinely have weak mobile signal and/or wifi? This is a big source of battery usage, and kitkat may be more sensitive to it.
2) are all location reporting services on, all the time? Have you analyzed how often your phone 'wakes up,' or syncs data? Does it happen even overnight when it is not being used (if still powered on)? Anything (apps, services) that tends to wake your phone even when not in use will drain. You may have to force stop/deactivate apps one at a time to see if that makes a difference, or use a battery monitoring/analysis app to help with determining the culprits.
3) Do you charge while powered on or off? Unlike the battery pull method, some folks have noticed that powering down the phone, charging it, then disconnecting before rebooting has made a difference. Something about a bad kernel in the charging software within kitkat causing the issue is what I recall.
In any case, you aren't alone, and lots of folks are hoping the next update to kitkat will address this problem.
