If I had to chose one single thing besides screen size, it'd be swipe typing. With Swype on my Note 2 I can type whole Word documents for work in an amount of time that actually compares to how long it'd take me to do it with a proper full-size PC keyboard. And it's an utterly elegant tool, very effortless. (The same keyboard also features an outstanding speech recognition mode.)
In fact I went down to the stores yesterday and tested some iPhones and iPads. It took me just a few seconds of typing to recall why I had gone from a 4S to a Note 2 in the first place. After getting used to Swype, there's just no way I can go back to thumb pecking. There's no way I can pass up that useful a tool for me. When it comes to text input, both iPhones and iPads now feel completely primitive to use.
Other things on my Note 2 that I wouldn't want to pass up are: split screen, Action Note and Scrapbook on the Note 3, homescreen customization (the sense of having a true homescreen, rather than an app drawer), the dynamic gesture functionality offered by Nova Launcher Prime and other apps, and the four at-a-glance widgets I always use on my two side screens, for calendar, Google Keep, Google Music and Flipboard. Oh, and the four toggle widgets which sit directly on my homescreen (small, unobtrusive, semitransparent) which allow me to insta-toggle airplane mode, mute sound, flashlight and WiFi hotspot - I don't need to bring up any other screen to get to these, and their status is always immediately visible.
I love the looks of the 5S and iOS 7, and I'd love to have that good a camera in such a small phone for quick snaps, but my Note 2 is just too damn capable to leave behind. And the Note 3 promises to be even better. If I just happened to have a spare $700 or whatever it is the 5S will cost off contract, I'd probably buy one to use when I go out partying, but that's about it.