The short answer is, low light motion. A flash is the only way you're going to get a good sharp picture in low light, if that is what you're trying to do. Even the 6+ pictures are going to sacrifice something in the picture in low light without a flash. Shorter depth of field maybe? I dunno, I really need to get my hands on one for a few days.
The long answer is, it depends on the circumstances. My Dad was a professional photographer so I grew up in the days of SLRs, light meters, master and slave flash setups, and the tricks of the trade back in the days before you knew instantly whether or not you got a good shot. I grew up "bracketing" shots: find the right shutter speed and f-stop for your shot, take a few pics, then back off a couple of settings on either side and take a few shots there, too. Think the Goldilocks method of photography. One shot should be too dark, one should be too light, and the other should be juuuuuuust right. If you knew what you were doing, that's usually how it worked out, too.
I try to do the same thing even today with digital cameras. If my subjects are willing and I have the time, I'll bracket a lot of ways. With flash, without flash, adjust exposure, etc. Then use Snapseed or similar to help make the final "dark room" adjustments to draw out the finished product.
I may be wrong, but I feel like the Note 4's camera improved its performance for me the minute I got done downloading all of the available shooting modes from the Galaxy app store, too. I hardly ever use those modes, but the camera seems to be much more responsive since I did it.
I know it isn't a perfect camera, and when people compare it to a 6+ they think it isn't as good. But as a lifelong photographer, I can say that I am pretty blown away by the capabilities of this camera. It is not too far off of the capabilities of a DSLR from 3-4 years ago, and in some ways it is probably more capable. And it's on a phone! It isn't always point and shoot friendly, right away, but once you learn how it functions, you can get some pretty rock solid shots with it.