While my Nexus did drain more battery because of LTE, my phone still lasted me a whole day with typical use. With my S3 I got to bed with around 40-50% battery left.
The S3 has the 2nd gen LTE which makes LTE a useful option since it basically doubled your battery life. (and I'm absolutely not going to do the disable/enable this and that nonsense).
I'm not sure what your typical activity is but it sounds similiar to mine. I usually can charge every other day with typical use on my 4S and probably a (6-8hrs) if I'm heavily surfing/gaming. Extrapolating from your data, with the 1st gen LTE it looks like it's 1 day of typical use and probably 3-4hrs of surfing/gaming. That just sucks.
This is my typical use on two work days. Mostly standby except for some call/texting/email in bursts. And look at my home's crappy cellular reception.