It's an evolution of the 2D Mario games, not the 3D Mario games. It's played in a very similar way, and the feeling of it is extremely similar. As for a true successor of the Galaxy series, I don't think this one is it. They usually try something completely new to succeed the previous major 3D Mario games, and this game is basically a sequel to the 3DS game. 3D World is part of the Super Mario 3D ____ series, where it incorporates everything we love about 2D Mario platforming, but in three dimensions. The true "next-generation" of 3D Mario will probably not arrive until a few years from now.
I think people need to quit with the "this is the true next -gen 3D Mario game" because it's not. It shares waaaayyyy too much with 3D Land to be the "next" one. The title, the art style, the mechanics of playing, I'm sorry but if you refer to a game that's that similar to 3D Land as the "true next-gen 3D Mario" then I have some bad news for you....