LTE is a known battery sucker for sure. By any chance can you post a screenshot of your battery usage (you can find this in Settings)? Perhaps it's something else.

 

This would be interesting to see. I've actually never gone a full day on LTE. At home and at work I'm always just on wifi so my battery is usually really good. I've noticed bad battery life when my signal is fighting between 4G, 3G and then 1X. If you can use wifi. It will save battery life for sure.

 

I haven't gotten around to doing it yet (maybe tomorrow being New Year's Day would be a good time), but since getting 4.1.1 I have been meaning to do a test of ALL settings on my s3 maxed out. I'm curious as to how long the battery would last in a day of my normal use if I use live wallpaper, have screen on bright, no Juice Defender, Power Save off, WiFi and Bluetooth always on, vibrate on everything, all of the little features turned on, etc. just out of curiosity.

 

You can always give Juice Defender a shot. What it does (to boil it down), is turn off the data connection while your screen is off. You can change that to turn on data every X time (this may be only for the Pro version).

 

I use wi-fi almost all the time and I have a live wallpaper and google now running with the location services. The best I have seen my battery run like that so far is 20h 44m 15s and I still had 37% left. Pretty good day with average use. Android system was 27%, Screen 21%, Android os 19%, Family Feud 7%, Idle 6%, Media Server 6%, and cell standby 4%. Seems pretty good to me but then again that's with a lot of wifi. I think if I went a whole day without wifi i would have to charge half way through the day

 

LTE battery life is actually BETTER than 3G battery life on Verizon. Based on my tests with two GS3s, an astonishing 50% better. That is not as much an issue of a great 4G radio as it may be that 3G (especially a low signal) is not too good on the GS3. If you have a good 3G signal it is not too bad, but AWFUL with low 3G.

That said, battery life is definitely better with the GS3 than the Razr was with 4G. The Razr though was better with 3G. GS3 also runs much cooler than the Razr did running 4G.


Added:

BTW, unless you live in the same area, use the same apps, the same app and data usage intervals and same settings on the device. Battery life comparisons are objectively pointless.