Dooley's UT team was far more talented than anything Jones had at Cincinnati. In fact, Dooley's UT teams averaged in the top 20 of recruited talent, while Jones (even though he improved the Cincy roster, and over-performed his talent) was in the 80's. The argument you just made would say that any coach who loses to another coach is automatically worse than that coach, regardless of the talent available. Talent matters, immensely.
Not only is your statement nonsensical but it de-evolves the more you look at it. You say 'So Butch lost to Dooley head to head, therefore Dooley is better than Butch.' However, Butch has beaten Spurrier twice, and Spurrier beat Dooley three times. Therefore, using your logic, Spurrier is better than Dooley who is better than Butch who is better than Spurrier. Is Saban a worse coach than Freeze, or Sumlin? He has lost to both, you know. If so, where are their championship rings?
You just found another way to show that the transitive property doesn't work in football.