Story-wise, this game is a bit of a disappointment compared to what came before it. I loved Super Mario Galaxy because it introduced us to Rosalina and she had a very interesting backstory. At its heart, the story was essentially another "Bowser has kidnapped Princess Peach, go and save her" affair, but Rosalina, and the tone of the game in general, gave a refreshingly unique, sombre feel to it. Super Mario Galaxy 2, meanwhile, barely uses Rosalina at all but is otherwise just the story of Super Mario Galaxy again, which is a shame.
Gameplay-wise, things are quite similar to last time. Each of the game's levels takes place in space as Mario explores small planetoids in his quest to find Power Stars, which he needs to find Princess Peach. Levels are often very creative, and gravity is regularly used in interesting and exciting ways. Movement feels very smooth and sometimes you'll be running and jumping through a level in 3D, only to be seamlessly moved into an area of 2D gameplay. Everywhere you go looks stunning and the game's bizarre scenery, such as a cube of water floating in mid-air, is very nice. The game has a very bright and happy design, which is quite a contrast to the rather visually dark feel of the last one.
Probably the best new feature that this sequel brings along with it is Yoshi. Yoshi appears in several of the games levels and is fully rideable. I always found myself excited when I started a level and saw a Yoshi egg in the distance. Riding Yoshi makes you able to move more quickly and he also retains his classic, comedic ability to eat enemies by catching them with his long tongue. On top of that, Yoshi has gained some new abilities in this game, for example there is something called a Dash Pepper, which seems to be a very spicy kind of pepper and when Yoshi eats it he runs forward at an unstoppable speed, making for some fun challenges. Luigi is also playable fairly regularly, and I like that, since I prefer Luigi over Mario.
On the whole, it did feel a bit like I was just playing Super Mario Galaxy again just with some new level ideas and without certain things that I liked about the first game. Super Mario Galaxy 2, however, is by no means bad; there's one area, which I won't say too much about, but it's called the Slimy Spring Galaxy and the combination of gameplay, visual design and soundtrack made for an absolutely sublime experience and this game is full of special little moments like that (though Slimy Spring is my favourite). Perhaps you'll play this sequel and think it's slightly better than the first game, and in some ways, I guess it is, but for me it felt like the original was slightly better. Nonetheless, this is a game that shouldn't be missed!