Great question about the Galaxy S3 and the ability to turn off 4G! I have this phone as well, so I can definitely answer this for you. With the Jellybean update, the ability to switch the S3 from 4G to 3G is no longer available. It was a capability with the previous operating system. The S3 will automatically go to 3G if 4G is not available, but the ability to change it manually is not an option with Jellybean. You have the option to turn off mobile data altogether if you want, by pulling down the notification bar and pressing "Mobile Data" so it is grayed out.
With regard to your battery, what is the change in the life of the battery since the update? Do you have any task killer apps on the device? How many apps do you have running on the device? I recommend backing out of apps so they are not constantly running in the background, using battery.
Hope this helps!
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