From reviews I still don't get if Super Mario Galaxy 2 is a must-have game if I have already played a lot of the first Super Mario Galaxy.
In what ways is it different from its predecessor, and how different is it?
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In one sense it's "more of the same" in that you work your way through "worlds" and "galaxies" finding stars and beating sub bosses to rescue Peach from Bowser.
However, there are differences:
the navigation between worlds and galaxies is different - you're travelling through them rather than visiting from a central hub.
You get to play as Luigi during the main game, either as a suggestion on random levels or eventually by choice.
Yoshi is available on some worlds.
The worlds/galaxies are all new - though there is some "borrowing" from earlier games. See this question
What happens (in terms of replayability) when you complete the game is different. See this question
If you really enjoyed the first one I think you should definitely get the new one. It's really well done, with more galaxies than last time, and way more stars. And, perhaps most notably, it is more challenging. Also, the "new game plus" content is great (more details with minor spoilers below).
After you manage to get all 120 stars the first time through, the game opens up 120 more stars, and for me the second set was the most enjoyable. They are just scattered throughout the levels, M64-style. You have to hunt them yourself--the only clue the game gives you is that they make a distinct sound when you're near them.
SMG2 may be more challenging than SMG1, but due to the enhancements to Player 2 it can be WAY easier to complete. Even the most challenging levels are reduced to kid-friendly explorations with P2 blazing a trail. If you're a parent looking to let you kid take P1 on a mind-blowing physics-defying platformer that perfects the genre, then it is a Must Buy.
One big thing is the transport from level to level. Adding on to that is the abundance of story throughout the game that is weaved into the gameplay rather than put into a book for you to read later (I meant that literally about SMG1).
Another big thing is that when you get all of the stars, including on the bonus world and prankster comets with the exception of the very, very last level, you can go through the game again but this time collecting green prankster comets. This alone adds about 8 hours to the game. When you finish finding all of those the last galaxy will open up and you can play through it. I have heard of a secret level in that world that I have been unable to find.