Q: What is qualitative superiority?
A: Qualitative superiority, also sometimes called being qualitatively greater, is a term colloquially used to mean that something is superior to an extend that it justifies being on a higher tier of infinity in terms of our Tiering System than the thing they are superior to. That means a character qualitatively superior to the usual spacetime continuum would, for example, be Low Complex Multiverse level (Tier Low 1-C) at the level represented by the R^5. Someone qualitatively superior to that would have the same tier, but on the higher level of infinity represented by the R^6 and someone qualitatively superior to that level would be baseline Complex Multiverse level (Tier 1-C).
In the same vein a space being qualitatively superior to another space, means that destroying that space would land you on a higher level of infinity in the Tiering System than destroying the space it is superior to.
In rough terms it means as much as being "more than countably infinite times greater in power or size".
The reason it is called qualitative superiority is that, instead of quantitative terms such as being 2 times, 100 times or even infinite times more powerful or greater, this type of superiority is typically justified by the nature of the superiority. The most standard case is dimensionality, where a difference in the quality that is dimensionality, implies the necessary quantitative difference. Another typical example is reality-fiction differences. Those are cases like viewing a plane of reality as mere fiction, like for example writing on a sheet of paper or a dream. They are assumed to imply superiority of a similar scale.
Of course, the same levels of superiority can also be reached via sufficiently explicit quantitative statements, such as when cardinalities above countably infinite get involved in a manner that implies a corresponding difference in power/size.
As the idea of "more than countably infinite times greater in power or size" implies, most statements of superiority wouldn't suffice to reach qualitative superiority, even if applied to already being infinitely stronger than the baselines for the level. E.g. being twice, a hundred or even infinite times stronger than a Multiverse level+ character, who already has infinite multiversal strength, would still not be enough to reach qualitative superiority over a multiverse.