Basically, I have 2 versions of a theory. This is like having two competing theories of complex numbers, one where $i^2=-1$ and the other where $j^2=1$ (hyperbolic numbers) or extending reals with $+\infty$ and $-\infty$ as opposed to only unsigned projective $\infty$.

The properties and value of these two theories are different. They have different algebraic properties. In one theory we have elements by which we cannot divide while in the other we can divide by all elements ….

That said, I want to post a question where people would express their opinions about which of the theories is more interesting and valuable based on their properties. We know that circular (normal) complex numbers are more valuable than hyperbolic (split-complex) numbers, even though both theories are entirely valid. Also, the extension of reals with signed infinities is more useful in analysis than the projective real line, even though in the latter we can divide by zero.

Basically I want to make a table that would show the differences between those two variants and receive answers that would argue about which properties are more important to have.

Is it possible to post such a question according to the site's rules?

thinkis valuable (an inherently non-objective criterion) will be opinion based, and hence likely to be closed. (But if MO history teaches anything, it's that the reception of soft questions is a very hard thing to predict!) $\endgroup$ – LSpice Dec 17 '20 at 23:27