Really good question. If you're talking about a Vitello-esque football coach, you have to go with the coach, as football stirs the drink at nearly all P5 schools.
The problem is that baseball just isn't a revenue-generating sport, even with Tony taking the program to unprecedented heights. This is going to be extremely unpopular, but as I've said in another post, living through the chaos and negligence of the Dickey, Hamilton, Hart, and Fulmer years, I think it makes more sense long term to have a good AD.