I own the 5S, the Note 3, and the LG G2 at the moment and will be downsizing eventually to just one. If ignoring all of the excellent aspects of each device and focusing purely on the camera on each, I find the Note 3's camera to be disappointing. I have obsessively put the 3 cameras to test in multiple neutral test shots using a multitude of different environments and the only situation I can find the Note 3 keeping up is in bright daylight. Once outside of that environment I find it to be the worst of the 3 and sometimes by a fair margin. I have owned enough phones in my time to know this is not because I have a faulty G Note 3. I am more than confident I could return this phone time after time and still yield the same results.
I am not saying the Note 3 camera is poor. As a camera on a phone it can take excellent shots. And if you take the time to dial in each shot, making sure you are using the right mode, with the right metering, and the right white balance....you can truly take some amazing pictures. But when I am trying to capture those unexpected moments, or when I am aiming for that quick picture....I am not putting in that time and effort. I am taking what the auto-shot gives me. And when compared to the cameras on the other two phones, the Note 3 gives me the worst of the three in that situation. Others may disagree and that is fine. I am comfortable with my judgment because I have taken the due diligence to truly put it to the test.