I'll agree there's some "apples and oranges" with regard to different theories.
This started off as a discussion that would (I hope) help clarify the issue of methodology. Looking at different theories for examles, it's easy to get caught up in the details of the theories themselves and end up with with "apples and oranges" comparisons. That wasn't my intent, and I've tried to avoid it but it can be a challenge when the theories themselves present so many opportunities for discussion aside from the original question.
Truly, some of these topics can range from A to Z, e.g. complexity. And worse, the correspondents are often speaking different math theories, so there is a tendency to get derailed.