For anyone over 50 that perception absolutely exists. For BYU fans who only pay attention when their team is being discussed, it's true.
But the national perception of BYU was the elite passing school that could beat up on inferior WAC teams but roll over when the big boys came to play. This was the linchpin that held up the BCS mindset. It helped justify the system.
Utah, without the tradition, challenged that mindset by breaking the glass ceiling.
While not as consistent as BYU certainly, the best Utah teams proved they can play with anybody on any given day. From the Final Four run, to the BCS wins, to OOC wins over BCS opponents, to bowl wins, to NFL draft picks, Utah was top of the class on what mattered to the big boys.
That perception of Utah is that we can play with them. Nobody questions that. While BYU has an awesome reputation and so forth, they still haven't jilted the perception of the little guy. Utah has. That's a huge distinction.
You can value whatever you want but I wouldn't say BYU "outshined" Utah.