The Note 2 is a very smooth device. Flipping between screens, scrolling, ect are all fast and smooth. There are quirks that I don't necessarily attribute to the hardware. It's either a function of touchwiz (samsung loader) or crappy app development for android.
Basically any app that is on both iOS and Android suck a lot more on Android. Slacker is terrible on Android. The fantasy sports apps are worse for yahoo and ESPN. Most music apps don't do lock screen controls. Lots of nagging messages asking about default apps (good and bad thing) and the wifi and cellular antennas are not as good as apple devices. Constantly get a bar or two less in many situations and the Note won't roam to the stronger access point like my iOS devices seemed to do better. Android also has a bigger issue with battery leaks (mentioned that in other threads too). My note burns 5% an hour in standby.
There's a lot I like that I simply can't get with iOS (or at least without Jailbreaking, if even then), but there's a lot that is frustrating too. I've said it in other threads but if Apple made a 5" phone I'd move back over to that side of the fence. App development, integration with things like BT profiles is better, and just basic reliability is better.