What's your typical smartphone usage ? To watch a lighted display without doing nothing ? I don't think so ...
I can use my iPhone, and I'm actually using it that way three times a week, for gps tracking while performing my running. Music is playing in background, running data are recorded, track is recorded, a lot of useful informations are given to me through the earphones (pace, heart rate, distance, time ....) .... and the screen is switched off. Is it an active usage ? It is !
CPU is working, data are exchanged, gps is activated ... a lot of things are running at full throttle but the screen is turned off.
An average SMARTPHONE user (typically text, mails, web browsing, phone calling and social networks) would have to charge the Note 3 on e a day too.
It has a bigger battery, but not so much better since the device consumes much more (bigger screen, higher frequency CPU, less optimized os).