To all the hundreds and thousands of people who are having battery draining issues with your S3's, I too, am having the same issue.
This issue is not caused by "too many apps."
This issue is not caused by using your WiFi, Bluetooth, or GPS.
This issue is not caused by faulty batteries.
This issue IS caused by Samsung.
With the OTA update to Android version 4.3, Knox was installed, as was an updated firmware for the boot loader and the radio (WiFi, mobile data, GPS, et cetera).
The radio firmware is the culprit. It was intentionally engineered by Samsung to cause this issue in an attempt to coerce S3 users to upgrade to upcoming S5 (since the sales of the S4 were way under projections due to customers being happy with their S3's).
That is why Knox was includes in that update, to prevent the firmwares from being rolled back to a previously usable state.
I fought with my S3 for about 18 months, eventually rooting and wiping all Samsung apps, and trying many different versions of Cyanogen and Paranoid Android. I even bricked it by trying to roll the firmware back, but luckily I was able to debrick it. It IS the radio firmware that is the cause.
About 18 months ago I snagged a OnePlus One and couldn't have been happier. This phone has been problem free for me from say one.
I've held onto this phone all this time in the hopes that either Samsung would fix this, or someone would find a way to roll back to the 4.2 versions of the firmware, thus, making the phone actually useable again. So far, no one has been able to solve this problem.
This is exactly the same thing that Apple did with the iPhone 3 and IOS 4. Intentionally cripple existing hardware to increase sales. It's why I personally will never use another Apple or Samsung product period. I even took out all Samsung monitors out of my office at work.
I refuse to give a business that does this another dime of my money.