Verizon just started pushing Android 4.1.2 to the Galaxy Note II. AT&T will start offering that same update to the original Note tomorrow, May 3rd.
Update: The word on the street is that this update is already available through Kies. Hook up and get it!
While the Android version bump is the same, however, everything else about this one is quite a bit different. Here's what you an expect post-update: