My Nexus 6 routinely gives me on average 5.5h Screen On time, and overall like 25 to 30 hours total battery life, and bad days I may only get 4.5h Screen On time with like 20 hours total battery life, but 9 times out fo 10, I get the 5.5h Screen On time.
Again, thanks to rooting and my tweaked custom ROM + Kernel ( Hells core beta 9 Mako ) and this ROM is 100% rock solid extremely stable, but makes the phone faster and smoother, and extends the battery life significantly.
To me my Nexus 6 giving me 5.5h Screen On is the borderline, of the minimum I need. Usually I find the 5.5h just barely enough to get me through the day, I need and want more battery life, because I hammer my phone all day and night long, couple hours of phone calls per day, million text messages, million e-mails, GPS Navigation, surf the web, watch YouTube, take photos.
Bottom line, if the Note 4 only gets around 4h Screen On time, that's terrible for a Phablet, phone would be useless for me by afternoon. Samsung screwed up big time, long gone are the glory days of the awesome Note 2 getting 6.5h to 7h Screen On time, the Note 2 was known as a battery champion king.