Android 4.0 with TouchWiz
Samsung has its own version of the Android 4.0 OS. The TouchWiz shell does have some nice extra features such as Pop Up Play (picture-in-picture playback of video content), S Voice (Samsung's version of Apple's SIRI van Apple and Voice Search from Google) and Smart Stay (the screen stays on as long as you look at it). It also looks a bit nicer than the standard version of Android, and you get seven home screens instead of the standard four.
The disadvantage of the TouchWiz addition is that Samsung has to create a new version each time Android is updated, and it can take very long between upgrades of TouchWiz. The end result for the consumer is that for example the Galaxy Tab 10.1 that came out almost a year ago, only last week got the update to Android 4.0. Since there is a pretty big difference between 3.2 and 4.0, that is a drawback for Samsung customers.
The Galaxy Note 10.1 comes with Android version 4.0.4, which is unfortunate timing considering Jelly Bean was just launched. It will likely take some time before 4.1 will be available, judging from how long the other updates took.