It is better for BYU (head-to-head wins, recruiting, etc.) for Utah to be the worst team not only in the state, but in the history of basketball. There might be wiggle room here if they were in the same conference and Utah's success meant better access and more money, but Utah winning tonight against Duke as a team in the PAC-12 simply does not have any direct (whether positive or negative) impact on BYU's basketball program as far as I can see.
So, my head says Utah needs to lose to avoid the possibility that they make a Final 4 (or worse, a national championship) while my heart generally guides me toward rooting for teams either from the West or with the lower seed (which would usually mean a team like Utah is a perfect candidate).
Thus my head and heart disagree and I find myself rooting for a 0-0 tie or a double disqualification or some other outrageous outcome I know can't happen as I try to avoid accepting that the inevitable outcome is that one of these two teams must win (and advance to the Elite 8) while my team lost in one of the most distressing ways imaginable.