Yes the Note 2 was the king of battery life, I agree, I owned the N2 for awhile, and it was a beast. But the Nexus 4 was at the other end, with total crap low battery life. My S4 is in the middle of those two phones for battery life, but little closer towards the N2 battery.
On average my Note got 8h On Screen time. My Nexus 4 got 3.5h to 4h On Screen time. My S4 gets 6h to 6.5h On Screen time.
hmm yesterday i used it for about 3hrs browsing web from 100% battery on my N5 ( no wifi ) and had something around 44% left on battery i believe