By new series you mean 2D Mario in general. Let's face it, apart from SMB2 USA, which was a reskin of another game, 2D Mario has been a progression of the same gameplay.
3D World is very much Galaxy without the gravity mechanics. The two are much, much closer to each other than Galaxy is to SM64 and Sunshine.
Galaxy actually retains a lot of the more open, or at least less linear, gameplay of mario 64. It's just usually confined to certain sections of the level.
Even in the linear courses, they frequently ask you to perform a platforming 'task,' in a small, but more open section (chompworks, clockworks, and melty molten all have this kind of thing). Think guiding the chain chomp along the path and collecting pieces of the star shooter, while still dealing with platforming challenges.
3d land and world, on the other hand, are virtually nothing but forward movement.
Nintendo even recognizes the difference between Galaxy and 3d land, which is obviously pretty important or there would've been no need to create 3d land in the first place.