I guess it's all subjective. I like the bigger screen, better battery life and the extra memory capacity with the microSD slot.
My goal was to have a device that would serve the purpose of both tablet and phone. The Note does that for sure. Battery life can also be amazing (compared to other Android phones).
But there are some cons. I list these considering how expensive this phone is.
1. Build quality is a bit iffy. Pick up a Galaxy S3 or Note 2 and compare to a Nokia Lumia 920, HTC One X or iPhone. Premium feel is subjective. Personally I don't like that my back cover creaks when I handle the phone and the buttons feel like they won't last the life of a two year contract. Before I get flamed, yes it's nice to be able to remove/swap the battery, I suppose.
2. The screen, while big and colorful, is not perfect. The Note 2 is WAY better than the PenTile arrangment on the S3 (so gross) and the colors are pretty punchy. However, AMOLED does not satisfy me as much as a good LCD (do yourself a favor and go see an HTC One X). There is some sort of latency/lag when scrolling slowly thru text and it drives me nuts. To be fair, I read a ton on my phone so maybe I'm picky.
3. If you like to try custom ROMS, look elsewhere. Yes, there are ROM out for the Note 2, but development is slow. I have read this is due somewhat to Samsungs poor documentation and support for Exynos chips (remember,the S3 has a Snapdragon processor). If you want to use the Spen, the ROM support is VERY limited. TouchWiz is not bad, but it ain't great.
It's not a bad phone and I don't regret buying it. But next time I will probably stick with a Nexus device.