It's not a matter of using it with one hand. In fact it's impractical to type a text one-handedly.
Actually, it's quite easy to type a text one-handed on a Note.
There's a one-handed mode that puts a smaller keyboard near to one side.
But answering a call? How do you hold such a large phone as the Galaxy Note III to your ear with a firm grip? It gets tiring after a while with a 3GS, and I do have normal-sized hands.
I think you think it's bigger than it really is. It's only about the width of a 3x5 note card, it's thin, and has a faux leather back that helps with palm grip.
I also have back-pockets that can hold this 3GS just right with its 11.5 height. A Galaxy Note III would technically overshoot the edge with its 15.1 height. Good way to lure pickpockets, or exert undue pressure on the screen when sitting.
True, the Note is about an inch taller and can poke out of a pocket.
However, personally I would never put a phone in my back pocket. That's just asking for all sorts of trouble.
Large also means less battery life if you want to keep the device portable. From what I get on an iPhone 3GS with "only" 3.5 inch screen, I prefer not to think about a phablet.
Google some battery test results.
The Note beats out the iPhone by quite a bit when it comes to battery life. Heck, it beats everything except the largest LG and HTC phablets.
Large means larger battery, plus the Note has some unique hardware to save juice.
Seriously, the reason the Note is so popular is because it packs a lot into a tidy, thin, light space.
Cheers!