I'm a bit surprised by some of these numbers. Not for what they are, but for the complaining about them. 14 hours with moderate use is pretty good for these fancy pants phones with 4G and high end CPUs in them. Here's a few reasons I've seen faster than usual battery drain on the S3 and even RAZR phones.
1) Network switching. That mobile data thing is always on in the background. If you're walking through buildings and it's trying to switch from 4G to 3G, back and forth, it will punch your battery hard.
2) WiFi goofiness. WiFi seems to be a weird one. Some people claim leaving it on lasts longer since it offloads the 4G connection sometimes. Other people claim that it drains the battery as it constantly searches for a network. I've got mine set up to turn off WiFi at work via an NFC tag, turn it off when it connects to Bluetooth in my car, but turn it back on when it disconnects from that same Bluetooth. Seems to work pretty well.
3) Screen timeouts. Turn down your screen timeout down. The more you look at that pretty screen, the faster the battery drain. Turn your brightness down and pick a background that is darker also.
4) Stupid apps. There are some apps that just love to sit in the background and trickle away battery. Yes, they only show as a small percentage, but if you have 20 of them running, they'll suck away your battery. If you're playing Words with Friends and getting your news fed with auto refreshing widgets, you might want to consider killing a few of those off.
5) Gestures, Smart Screen, Air View. Figure out which of these you actually are going to use. If you don't actually use them, shut the feature off. The sensors that feed data to these are battery drainers.
6) Disable any stupid built in app you aren't using. If you're not an Amazon MP3 user, disable it. If you use Google Maps, disable that Verizon Navigation app. Once you disable all the ones you don't need, reboot your phone. In most cases, with the app disabled, some of the pointless background services that feed them will not be started when you boot.