BYU clearly has a greater academic reputation, prepares students for graduate school better than any university in the country, and has a unique mission and experience (especially for LDS kids).
That doesn't make it "greater."
I'm a professor at what you might consider a "lesser" school (SUU), and I love it here and have no desire to ever teach at BYU and live in Utah valley (I've had opportunities to do so). I like living in a smaller, more isolated town. I like our rural student body and the farm boy work ethic. I love that I have a ton of autonomy in my teaching and can be innovative and stray from the norms. We also have a great student body, a good institute program, and an incredible community.
I also have four children that I hope will choose to go to college. Two of them I think would be a great fit at BYU, and I believe one of them would do much better at SUU or a similar university (the other child I have no idea, she's just 8).
I'm a pretty hard-core BYU fan despite having attended or taught at seven other universities. I love the BYU mission, BYU athletics, and the BYU community. I love it so much that I regularly talk about BYU football on the radio and write articles about the Cougs on various sites. I try to make it to at least one game every year. I defend BYU in online forums and encourage kids to consider it as a great place to get their education.
But I don't believe it is a "greater" school for everyone, and cringe when others talk about BYU in that way. That kind of attitude from the BYU faithful feels very condescending, off-putting, and unnecessary.
Let's just recognize that people are individuals and there are great fits for many students that aren't BYU.
Go Cougs!