How does Super Mario Galaxy 2 differ from Super Mario Galaxy?

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.