BYU
1 National Championship
1 Heisman Winner
2 Outland Trophy Winners
1 Doak Walker Award
52 All Americans (13 consensus All-Americans)
18 top 25 finishes
23 Conference titles
Utah
0 National Championships
0 Heisman Winners
2 BCS Bowl Wins
0 Outland Trophy Winners
0 Doak Walker Awards
32 All Americans (6 consensus All-Americans)
10 Top 25 finishes
24 Conference Titles
So looking at the overall resume... BYU is far ahead. Currently Utah is playing better football. But I have a feeling that's going to change soon.