I have the III and my daughter has the Note 2. Her processor is a little faster (Negligible, IMO) and the resolution is exactly the same.
She has split screen, but I have burst mode on my camera and NFC capability. The one factor that changed my mind and made me wish I had the Note 2 was the HDMI to USB capability. Other than that, I prefer the size of my screen as more one handed friendly than hers.
How strangely will the Tools of a Tyrant pervert the plain Meaning of Words!