1. I can tell you that it's not KitKat itself. MANY people have been using it on the S4 without problems. I've been using it on my Note 3 for a long time and get excellent battery life. (I don't use it especially hard, but I usually get at least 36-48 hours per charge if I don't do more than check a few emails and look for answers to questions here - like where is X in Settings sort of things. If I make a few calls and spend a few hours playing solitaire [doctors' waiting rooms are boring places], I still get more than 8 hours.)
2. Back up everything (see
Backing up an Android Device) then do a factory reset. Restore everything (you'll probably find a lot of apps you have on there that you no longer use - you don't have to restore them now, you can always restore them later). Give the phone a few days to "settle in". Then your battery usage should be good.
3. Check your signal strength. Settings/General/Battery. Tap the graph at the top and look at the Mobile network signal line at the bottom. If it's not solid green, it'll cost you battery. (If the signal is weak from the tower to the phone, the system assumes it'll be weak from the pone to the tower, so it increases transmitter power - and that eats battery in a big way.)