Utah beat four ranked teams that season; two that finished in the top 10. Including a decisive victory over one of the most elite programs in the country.
While 2004 Utah was probably a better overall team, in terms of the quality of wins, it doesn't come close to Utah's 2008 run.
1984 BYU may have had the best of any of those teams, but has the same issue as Utah 2004. Maybe worse. In terms of national recognition and credence, I think most people would take Utah's 2008 run.
Overall, I'd favor BYU's accomplishments personally but the recency of Utah's success and the higher quality wins have a lot more value to mainstream CFB fans than you think. The two programs are far more comparable. When you factor in the collective strength of Utah's Bball program, I really don't see a fair argument that BYU's brand is significantly higher/better/more prestigious than Utah's.