I just turned my phone on 15 minutes ago and checked the battery status in setting and it shows that media is using 62% of battery. My battery has drained 12% in that 15 minutes. I have diabled just about everything that I can think of and still no luck. This is a US verizon s3 and their customer service just gives me the run around. Verizon needs to find the problem and get it fixed. It seems to be one that everyone is having since the jelly bean update.
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