Hmm... Well, despite all the power of Higher-Dimensional Manipulation, my main concern with that would be that it would be practically incomprehensible, and so would be very difficult to use.
Immaterial Manipulation, on the other hand, is not only a lot easier to comprehend, but also has the potential to be far more powerful. I mean, the presence of Axiom Manipulation alone makes this an immensely powerful ability. Since Axioms are things that are objectively, inherently and self-evidently true (unlike normal 'truth' which is arguably very subjective) by changing them you can fundamentally alter how reality functions. For example, make it an Axiom of yourself that "I am whatever I choose to be", and you've effectively gained virtual Autopotence. You can rewrite youself to be anything you want and have virtually any ability you want.
And then there's things like Boundary Manipulation, Concept Manipulation and Metaphysics Manipulation, which all make Immaterial Manipulation so much more powerful.
Higher-Dimensional Manipulation
Immaterial Manipulation
