The Camera app has been enhanced with the kinds of image-correction features increasingly found in digital cameras, such as the ability to select each person's face in a group photo and choose the best version from a series of exposures. There are more such enhancement capabilities than in an iPhone 4S or 5, though the Note II doesn't have iOS 6's autostitching that assembles panoramic images from a series of photos.
UI improvementsIn all apps, the Note II's onscreen keyboard gains a fourth row at top for numerals (like a physical keyboard), which further facilitates text entry, though it reduces visible screen real estate too much in horizontal orientation. And a long-standing beef of mine is addressed: In the notifications pull-down, you can now tap and hold the Wi-Fi icon to select a different access point, not just use the icon to turn Wi-Fi on or off as in standard Android. (The Galaxy S III also gets this function in the current Samsung Android 4.1 update.)
There's also a new setting for one-handed operation, which reworks several UI components so that they're clustered in reach of a thumb. One of my critiques of the original Note was that its screen was too large for my thumb to reach all areas -- and my hands are fairly large. This new setting is meant to address that reach issue. You can now move the Phone app's buttons, the Calculator app, the onscreen keyboard, and even the unlock window to one of the lower corners, based on whether you are left- or right-handed. But there is still no split-keyboard option for two-handed thumb typing, which would be a helpful addition.