Yuriman - I'm guessing the Moto X is counting some sort of active notification, like the time always being on with a black background, as 'screen on', not what most of us consider screen on.
First - you're time off battery = screen on time which would normally be impossible unless you're doing something on your phone 100% of the time. The lack of apps showing up in your battery usage list (wifi being second, Android OS next, Cell standby for goodness sakes) basically shows you're not actually doing anything on your phone - it's in what most of us would consider standby, but b/c of the active notification, it's being considered screen on.
Then, the nearly straight line of battery usage over 15 hours and again where off battery time = screen on time. 'Normal' battery usage is a series of slopes and horizontal lines as the phone is used and then put down. Your WLD screenshot actually shows only about 20 minutes of app usage.
So if I'm reading this right, your battery life isn't actually that impressive - 15 hours off battery with generously 30 minutes of actively using your phone is pretty bad. The Note 3 would easily last 2 days under the same working conditions of barely being used and 6 hours of actively using the phone on calls/apps/etc.