Previous phone being the Note 2, I don't see a *huge* difference between that & the Note 3.
I love my N3 and will definitively get it again (if you can afford it), battery life is just AWESOME as is the screen and its size (for my old eyes
), and i love the S-Pen. Then, there is
nothing you can't do with that phone and i didn't need to root it (t-mobile version but i use Metropcs, same thing but far cheaper).
As many mentioned in the forum, some of the N3 features are just ok: camera is good but not that great, reception is not that great either, sound is just correct, issue with a bug with SD cards, S-voice sucks and you can't switch to anything else, GPS and accelerometer are not great, etc... but there is nothing bad with it.
Frankly, i see a friend with a N2 and he is doing all the same exact things that i do and his photos are a bit better (despite lower resolution), so it's a faster but not that much improved version of the N2 and if you are on a budget, N2 are more affordable and same battery life!
If you don't need the S-Pen or a huge battery, go for something different: the HTC One is awesome or the Nexus 5 which is the best you can get for you money (unless the OnePlus One becomes available)!
Else, i highly recommend the Note 3.