Well...
*there are some new characters
*the planetoids are more vivacious and lushious
*Yoshi is introduced as one of your partners (including special fruit power ups for Yoshi, which are vital to passing parts of the galaxy)
*Its more challenging compared from the first Super Mario Galaxy (even though i finished SMG2 in less than 2 days in hours. >D< )
*All sorts of new power ups (also vital to passing parts of the galaxy)
*More stars to collect
*New challenging puzzles to complete the stage
(those were from the top of my head =w= )
...But overall, i loved SMG2. The only thing i dont like about SMG2 is that Rosalina (princess of the galaxy. shes my favorite girl character.) doesnt show up that much. She only does if you die SO many times on one mission, she'd help you (heh, she was like Cosmic Mario, but it was Cosmic Rosalina

) get through it, but if you let her do that stage for you, you'll only get a bronze star, instead of a gold one. The only other appearances ive seen of her in the game is when you finish it, and she congradulates you, and tells you shes proud of you.