People are also saying that the iPhone 5 takes vastly superior pictures, but based on this thread,
http://forums.androidcentral.com/samsung-galaxy-note-3/341247-note-3-vs-iphone-5-camera-samples.html, I'm not seeing it.
My honest opinion is that it's all subjective and people will see what they want to see. My guess is that there's an iPhone forum somewhere that someone is proclaiming that the Note 3's camera blows the iPhone 5's out of the water. I'm also guessing in that thread there are probably some people that want to appear to have such impeccable and distinguishing taste that they insist the iPhone 5's camera is abysmal.
I don't claim to be some sort of camera snob, but if I did I think I'd probably try to focus my expertise on something more formidable than a camera phone. I find it akin to trying to convince people that I'm an auto-performance enthusiast because I think a Honda Accord handles better than a Toyota Corolla. In the end you're still using a cell phone to take pictures.