Hello, This is also happening to me. I came here for this very same reason. Since the update, my phone can't hold a charge for nothing. So disappointing, when that was something that I really liked about this phone in the beginning. I hope they find a fix for it soon.
I am really beginning to wonder if it has to do with the radio/antenna? I posted a question earlier in the week about what effect the "global" radio had but haven't gotten any responses. I say this because prior to JB, I tended to keep my phone on 3G (CDMA/auto PRL) to preserve battery life. I would put it back to 4G (LTE/CDMA/EvDo) only sometimes, at night when working my 2nd job up north. Now since JB there is a "Global" option that wasn't there before with ICS and it is a defaulted selection. Since I had trouble switching and stuff, I decided to leave it on Global and leave it alone. Now a few good days into leaving that alone, I see my battery life stinks. I think I may go back to 3G only and see what happens.
Do you have some sort of picture backup service enabled? If that's not working properly for some reason, that may cause high battery drain.
In other postings on the Android forum they said it was the radio now being turned on to Global settings. And turning it off made a difference so it was not searching for those signals. Switch it to CDMA and try that. On the Galaxy S3, settings, more settings, mobile networks, network mode, choose LTE/CDMA.
Setting the radio from Global to CDMA/LTE seems to be working well so far. I will give it another day, but I think that was it.
I also noticed significantly increased battery drain after the update. I switched my Network to CDMA/LTE also, but I think the real killer was a couple of other settings that the update (re)enabled that I had turned off; the SmartStay option in the Display settings, and the option in S-Voice settings where it continuously monitors the microphone, waiting for you to say the 'magic wake-up command', that one even says it will drain your battery! With all that stuff on, my battery usage list would show "Screen" as the top item, and that was with the phone sitting untouched in sleep mode for several hours! I also found a couple of the "location update" related settings turned on that I was pretty sure I had disabled. I'm not sure which of those made the most difference (I suspect it was the S-Voice thing), but after putting all that back to way I had it, my battery usage is back to normal.
Many people in the DroidForums discussions are saying they had to do a FDR to fix this, but I suspect all that is really accomplishing is turning off all those battery-eating settings that the update (re)enabled. If anyone is still having issues after switching off the Global radio setting, I'd try the stuff I mentioned first, and if you still see battery drain with your settings back to pre-update values, maybe try the factory data reset.