It's weird, it happened to both my phone and my husband's phone the same day. Usage hasn't changed and I didn't download any new apps. When I check usage, it's usually either Google Core Apps, Google Services, or Android OS using about 60% of my battery power. My battery life dropped from 20-25 hours to 6-7. I've tried Juice Defender and Battery Doctor with no luck. It literally started the day after we accepted the system update.
Have you had any luck finding a fix? I'm starting to wish I hadn't gotten my s4, as I now have to carry my charger with me so my phone doesn't die. My old LG Marquee had better battery life.
Finally was able to fix my battery life with a factory reset. Making me really weary about the next system update...
I'm rooted on MF9 and don't really have any problems at all. I also don't have any bloatware. I have the native hotspot mod working (love it!) And any app I want in the multi window. The battery lasts all day on heavy use though I do run Snapdragon Battery Guru. I'm not even sure if that really made any difference because it lasted a whole day on one charge before it got any updates.