The Note 3 is not iPhone 5s primary competition. These are 2 very different animals and are geared towards different crowds. Your basically comparing a Honda Accord to a Chevy Suburban. I don't believe Samsung makes the Note devices to compete with their "S" devices or the iPhone directly. All Samsung is doing is offering choice; something Apple is afraid to do. It has flagship specs but it will never beat the Galaxy S4 or iPhone in sales because those phones appeal to more people.
The only phones that can compete with the Note 3 would be the 6.44" Sony Xperia X ultra, the 5.5" LG Optimus G, the 6.3" Samsung Mega and the upcoming 6" HTC One. The 4" iphone is not in the same league. The bottom line is that Android has too many weapons to choose from. I would find it embarrassing if Apple gets beat by one model because Android users have better selection compared to last year.