I'd go with the Note 3, its better all around and its newer. The Note 2 will is going on 2 years, why spend money on such old technology unless you can get that phone really cheap.
Well, when I buy anything, I always buy the latest so I would go for the note 3. By the way, I had one and it's awesome! I never tried the note 2 so I can't compare. I'm too dependant on the Apple ecosystem so i went back to an iPhone but it wasn't because I did not like the phone, I really liked it, I didn't use the pen that much but I was glad it was there.
I have had all the Galaxy S and Note series since release and I can tell you the Note 3 is so worth it over the S series but the S5 does make it hard to decide. I would take a look at the Note 3 and S5 once it comes out but if you're really into a big screen and can wait then the Note 4 would be the phone to get. Or you can do what some folks do is get the S5 then upgrade to the Note 4 once it comes out. I've been doing that every year but hopefully this year I can resist the S5 and just wait for the Note 4.
It depends really, I bought a note 2 for less than half of what a note 3 costs, and I'm happy with it. I actually prefer the rounded edges of the note 2 but in all other departments the note 3 is much better.