iTunes 11 - Difference between "Play Next" and "Add to Up Next" buttons

Solution 1:

'Play Next' adds the song/album to be played directly, 'Add to Up Next' adds the song/album at the end of the songs/albums that have already been added to Up Next. For the first song/album, this will make no difference, but try adding a couple more and you'll see the difference.

In other words, 'Play Next' works as a stack - Last In First Out, while 'Add to Up Next' works as a queue - First In First Out.