I voted Prohm, because from what I have read I am starting to get on that train.
You want a guy who wins. The best predictor of success is prior success. Hoiberg was a winner at everything he had done, despite no coaching experience. I think that's what JP saw, and he was right on that.
Prohm has a hell of a record, albeit in a smaller pool. Can he make the jump to the Big12? Who knows. But he sure whipped up in AAA ball, so a shot at the big leagues seems reasonable.
That is not a perfect predictor of course, e.g. Greg McD. But it is still the best single thing to look at.
So I guess between Prohm and TJ, the question is - do you value the head coaching experience more than the Big12 experience, or vice versa?
For me, I think it would be great to have both, with TJ as a great recruiting assistant for a successful head coach. Seems like best of both worlds. Unless the job was promised to TJ and it pisses him off not getting it, and it becomes a cancerous situation. That would be bad.
Hiring is always a crapshoot, you do your best to limit mistakes and hope you don't make one.