I Can Be Your Hero makes a valid point. The majority of the market simply wants an easy to use camera that they can pull out of their pocket and take a picture.
The only time most people have their DSLR (if they even HAVE a DSLR) with them is for sporting events, school functions, holiday/family gatherings or the like. For any other time, most people only have their phones.
Having said all that, other than the low light motion issues, which any camera struggles with (even the iPhone 6, which clearly does better than the Note 4 with low light motion) the Note 4 holds its own very, very well. In a quick google search of "iPhone 6 vs Galaxy Note 4 camera" articles, most scored the cameras pretty even. The one article that I found which declared the iPhone a "clear winner" is a head scratcher because the photos they used for comparison, the Note 4 and the G3 were better in every one of them, but the author chose the 6 anyway. I can only assume that either A) the author has no experience with photography or B) already owned her iPhone 6 and therefore was biased in that direction anyway. The rest of the articles were "no clear winner, they all have their strengths and weaknesses" for the most part. I discounted most "pro-Android" or "pro-Apple" sites from my search, even though I read them anyway. I was hardly surprised an Apple blogger thought the iPhone 6 "blew away the competition" any more than I was surprised by an Android site saying the Note 4 was "superior in every way."
With my photography background and experience over the years with SLR, DSLR, PnS, and camera phones, I can't claim to be a "typical consumer" but I am no different than anyone else of only having my phone with me the majority of the time. I don't know if it is because of my experience as a photographer or not, but I have found the Note 4 camera to be a better camera in almost every situation than the iPhone 6. The only place the iPhone is a better performer is with low light motion, but even then the pictures are not great. Low light situations, by definition, require some sort of flash to compensate. Even with a flash, the Note 4 doesn't perform as well in that same situation--but the gap closes considerably. Enough that I can't say "clear winner" for either phone, but I give slight nod to the iPhone. It gets it done. The Note 4 is okay, and apps like snapseed will help enough that I wouldn't tell anyone to buy the iPhone 6 over the Note 4 only because of this one particular aspect.
For any other situation where someone will find a camera phone a useful tool, neither of these phones is going to stand out so far ahead of the other that I would declare one a "clear winner" over the other. I do think the Note 4 is an overall better camera and is capable of much better pictures, but that is offset by the fact that you do have to "set up" your shot from time to time. That can be a difficult thing to do with sports, little kids, pets, etc who often are not the most cooperative subjects. If your subject is stationary or the lighting is excellent, however, you have a camera that can almost compete with some DSLRs on the market today--and certainly compete with many PnS devices.