Notre Dame is one of the winningest college football teams of all time. You can't say take ND for example in comparison to Utah, BYU, or really the majority of college football teams out there.
It'll take a little more than a few years of up and down to knock them off that pedistal, but if they continue this pattern for another 10-15 years? Who knows? My generation does not consider ND a national power at all. Historically impressive? Yes.
BYU resonates with those 30 and older for their dominance during Lavell's time and rightly so. Thus, they have recognition and popularity (the Church I think is where popularity, fanbase-wise, is founded).
That being said, if BYU does not make it past October with 1 loss or less, their season is over for all intensive purposes. They are not in the BCS discussion and no one they have scheduled in November is helping that cause.
Utah on the other hand is hitting their stride as far as making waves. They have the 2 BCS Bowl wins (which DO resonate with my generation and college football fans), has an all-star head coach that is widely respected and admired amongst other coaches and analysts, has stepped onto the Pac 12 scene as the only real threat to USC's South Division title shot (at the moment), and can still be part of the BCS conversation late into the season with as many as 4 losses in-conference alone (last year anamoly).
There is no question who the more relevant team in college football is right now between the 2 schools and any attempt to argue it resembles personal experiences that Y fans have had with an out-of-towner a time or two.
I imagine this is how Utah fans acted in the late 70's when BYU was taking over and Utah had only history to back their claims. I wouldn't know. 1986 born baby!!! Go Utes