aside from the fact he is more likeable, he has been more successful than Bronco. Rose (1) lands almost all of the top LDS four star recuits' and (2) wins 20+ games and makes the big dance pretty much every year. Bronco does not land the majority of top LDS talent and does not win 10 games every year. When he did win that many games, he was a fan favorite.
If Rose were to start losing out on the majority of big recruits and BYU were to start winning 15 games a year, you would see the fan base turn on him pretty quick IMO.