In addition to all of the above, which I agree with, an additional tangible consideration is that flying out of an airline's own hub reduces the number of cheap flights and mileage run opportunities. DFW is not much of a starting point for a MR on AA, for example! However, they often have some real bargains out of DEN.

That leaves the intangibles: Others may have different opinions, but I find that OW just WORKS better than *A. There are fewer hassles with checking baggage all the way or getting boarding cards on multiple segment trips, my points earned on partner airlines post more reliably, airline staff tend to extend courtesies according to status more cheerfully, etc. YMMV, of course.

I have the same status level on both and pick the flights that suit me on a case by case basis. If you fly enough, you should try to spread your business.