Verticality and more going on, but also hidden areas to discover, and tons of objects you can possess with each have their own properties.
3D World actually has a ton of hidden areas, some of them even can be hard to find iirc. But yea, there's nothing like the possession mechanic.
One thing I really dislike about 3D World is how inconsistent its levels are thematically. Each world has its own theme, you have the water world, the ice world, the cloudy world, etc, but then it's always just the first stage that fits the theme of its world and then the other stages are just variations on other stages you found in different worlds. It kinda ruins the immersion of the game, makes it seem like nothing more than just a set of challenges for you to overcome, which itself is kind of an issue since there's pretty much zero challenge during the game's first 5 worlds and the difficulty curve is basically a flat line.
I know that Mario games aren't known for their immersion, that's not what they're supposed to be best at, but personally I really can't care about a videogame if I'm not invested in anything that's going on in it. It's just worse when you compare it to another linear platformer that came around that time, Tropical Freeze, which had masterful level design and worlds that felt entirely cohesive, with each level being part of a larger "story". Without needing to have any actual narrative.
Odyssey is a lot better at this, it's a game I could actually have some investment in. But personally, I'm never truly gonna care about Mario.
Yea that's a part of 3D World I'm not really keen on either. I think it was even mentioned in reviews of the game at the time. It's a bit hard because, part of the problem is that no single world theme in Mario games is super interesting, and with how much content they tend to pack into each world, you'd basically just be asking for more worlds at that point. At the same time, it doesn't exactly feel immersive or organic to have an entire world for each type of possible theme. There's probably creative ways around this but Nintendo didn't take them. Nintendo's world design kind of sucks.