People need to adjust their expectations when coming from the iPhone. No other smartphone camera takes pictures as quickly as an iPhone can in low light. The iPhone has larger pixels than any other smartphone camera, which can take in more light at once, and thus has the fastest shutter speed in low light since it doesn't need to keep the shutter open for long to receive all the light it needs, thus reducing blur. The sensor is "only" 8 megapixels because each pixel is bigger than normal and takes up the same amount of space as most 13MP cameras on Android phones. The iPhone's pixels are1.4/1.5 microns big as opposed to the smaller 1.1 micron average. It will obviously still pale in comparison to the comparatively gigantic ones on a DSLR and be slower and noisier, but it is well ahead of other smartphone cameras otherwise.
The Galaxy Note 4 relies heavily on longer exposure and slower shutter speeds, leaning heavily on its optical image stabilization, to take low light shots. They actually overdo it and leave it longer than it should, resulting in overly bright (compared to the actual scene) and glowy pictures from overexposure. This means any sort of motion within the frame will blur. Cameras like the Galaxy S4 that don't have optical image stabilization will instead jack up the ISO and take noisy but fast shots. It's a delicate balance between ISO and shutter speed and unfortunately for many, Samsung and many others that have optical image stabilization will opt to use slower shutter speed and lower ISO to take a bright low light shot that blurs any objects that move. Whatever ISO settings they may offer won't override the default tendency for longer shutter/exposure. The only way to remedy this is being able to set your own shutter speed, which won't happen until the Note 4 gets updated to 5.0 Lollipop and you use a third party camera app that allows for fast shutter.
Also the theory that there are different sensors/lenses is untrue, unless you buy an international model of the Note 4, some of which include an ISOCELL sensor instead of the IMX240. The US models should all be identical. Neither of them are that different from each other and it won't change the way Samsung has programmed their camera software to rely heavily on longer shutter/exposure.
If fast low light shots is a high priority, the iPhone is much better for this.