I've had my S3 for just a week. I did an OTA update to Jelly Bean. The battery seemed to be doing pretty well. However, last night, I charged the phone to 100% prior to going to sleep ~ 1 am. When I woke up @ 7 am, the battery was @ 40%. WTF?? I didn't do anything differently. I didn't have any processes running overnite. My phone is connected to my wireless router. My prior iPhone 3G never experienced such a rapid battery drain. I charged it up to 100% @ work ~ 1000 am. Now it's 6 3/4 hrs later and the battery is @ 75%. My phone connects to my workplace wireless. I keep bluetooth on all the time (as I did with my prior phone). I did also notice that when I got home around 6:30 last nite, the phone was @ 40%, but within a couple hours, it drained to 7%.
I hope last nite was just an abberation. I'm going to see what happens tonite and the next few days.
Update 1/24/13:
When I got home ~ 740 pm, battery @ 64%. There was a rapid drain to where the battery was dead ~ 1 am (6 hr later). This only happened the last couple nites. Here is a screenshot:
Where it says "14 h 5 m..... battery", right above the "e" in "battery" is probably when I arrived home. You can see the more steep downward decline. I disabled Samsung push as someone suggested above. Tomorrow, I will take the battery out and reseat it.