The special stages have design flaws and are not as good as 3K, blue spheres are the fucking GOAT it's not even close. Mania does not have good story progression and the stage transitions are extremely weak compared to 3K. 3K feels like a grand adventure, has great pacing and comes to a satisfying conclusion. Storytelling in Mania is absolute arse in comparison and the game does not end on a high note. I would also say that the level design, while generally great, does have CD like problems and often feels to big. Doesn't quite nail that balance of exploration and tight stage design the way 3K does.
3K also implements bonus stages better. Blue spheres are amazing, but they're too long to be suited to be played every minute. Hurts the pacing. 3K's bonus stages were quicknand anappy and suited that format better. Blue spheres suit the hidden ring formula, not the checkpoint activated one.