I can't compare the N2 and the N3 because never had the N2 but I had the S4
Compared to the S4, the N3 gets better battery life even with a beefier processor and a bigger screen, but for me it's a 10%-15% difference
The odd part is my S4 on Verizon seemed to discharge slower, compared to my N3 on AT&T but that could be because I work in a basement in NYC and on Verizon I got 3-4 bars with by S4, while the Note on AT&T gets 2 bars.
Unplugged my phone at 7:30 am today and wifi on, vibrate on, GPS off, NFC off, BT off, Power saving mode on, Sync off, air gesture and other gimmicky Samsung stuff off, auto brightness on, LTE 4G on, I have done 4 hours and 30 minutes and 29 minutes screen time. This seems good but nothing like what others have been claiming to get. My feeling is this has to be due to the mediocre LTE signal . Going to continuing to monitor through Gsam Battery Monitor and take screenshot at the end of the day then test out the battery life this weekend when I am not in a basement and have better coverage and take a screenshot.
I am just concerned my N3 might have a rapid battery drainage problem.