As you have mentioned camera & battery life as important, S3 would be a good choice among the 4......
N4 is good for just performance, with average camera & battery life for the price
But try to get SONY Xperia ZR @ 24k (same performance as N4 + better camera than S3 + better battery life than S3)
Deal Of Week 05: Sony India Warranty Xperia ZR - Water Resistant | eBay
Sony Xperia ZR battery life test breakdown - GSMArena Blog
My experiences with ZR:-
I originally bought the phone to play games in it but when you have a laptop with dual GT650m , you don't give a damn so I stopped playing games in it. Camera Quality is awesome but then again when you have a Canon 600D, you give zero damns.
Now I regret buying a phone with such a low screen size because I mainly browse and stuff. Buy this phone only if you are into mobile gaming as it has a quite a capable GPU, my friend was jealous that Angry Birds Go! ran in my phone with enhanced anti-aliasing.
This phone is very sturdy and build quality is awesome, dropped it twice already and once on wet bathroom floor.
Also, this phone runs quite hot while playing games like Modern Combat 4. There is a solution to this:- Throw it in a bucket of water, seriously. This phone is fully water proof(make sure all flaps are closed), I have kept it in a bucket full of water for a full 5 mins many times.
Battery Life is awesome in Stamina Mode :- Survived a whopping 2 hours in standby mode when battery charge was 1%.
Btw camera is pretty good and it supports Virtual Reality which was advertised in Xperia Z1.
The best thing about this phone would probably be Mobile Bravia Engine 2 which enhances the quality of videos, thus making is pretty much the best phone(in this screen size T_T ) for viewing HD videos.
BE 2 is possible in other phones but that requires rooting etc.
Also, unlocking the bootloader in this thingy is easy and a custom rom of Kitkat has already come.(Tried it :- no BE 2 + no stamina mode so went back to 4.3 US version).
