For me the Note 3 was a tremendous upgrade from the Note 2. Having the two side-by-side with plenty of time to compare revealed for me the shortcomings of the Note 2. (That's not to say it isn't an excellent device, just the Note 3 outclasses it by a long shot.)
The Note 3 has a bigger/sharper screen, without adding much dimension to the phone. It looks damn near perfect IMO, revealing to me that the N2 was more of a compromise design.
It's thinner/lighter, feels MUCH better in the hand. After getting the N3, my N2 started to feel like a brick in comparison.
The S-pen is more responsive, has better features, is that much more useful. Everything is fluid and smooth (although I'm sure someone will manage to obsess over something, somewhere on it lagging, but then those types do that with literally *EVERY* device ever made by anyone, it just depends on which agenda they are pushing as to which device they nitpick to get obsessed over. In other words, extreme nitpicking has become a truly useless measure to judge the actual speed/usefulness of a modern device.)
I fail to see what amount more speed/horsepower anyone *really* needs in a smartphone on a practical level at this stage in time. I can't imagine what anyone would be doing witha phone right now that requires all that much more. (Now, maybe in 5 years when everyone is doing 4k video editing on their smartphone, sure, we'll need more horsepower for that. But since that's not 2013's reality...)
I'm sure there may be something faster/better just around the corner, but then there always is. IMO, the N3 is a fantastic upgrade to the N2, especially if you were very happy with the N2 as I was.