I hate to rain on nearly everybody's (BYU and Utah fans) perception, but the required public reporting of athletic budgets for the most recent year available shows that BYU pays its men's coaches more than Utah pays theirs. At least, that was the case a few months ago when I looked.
The view is broad, but this information is far, far, far better than what you heard from an ALUF, you're home teacher, that guy who works in church IT, or just about anything else.
The myth that Utah pays much more than BYU is totally unfounded.