I was bored earlier, so I decided to do a bit of research that I thought I'd share. In the past 11 years, the series sits at 8-3 in favor of Utah. Utah's largest margin of victory is 44, lowest is 1. BYU's largest margin of victory is 7, lowest is 2. Utah sits at +108 in the point tally, BYU -108 (obviously). Utah's total margin of victory (in wins only) is 120 points, which works out to an average margin of victory of 15 points. BYU's total margin of victory is 12 points, which works out to an average margin of victory of 4 points. BYU has won at Utah once. Utah has won at BYU three times. Utah's overall record since 2002 is 94-34, with 10 seasons over.500. BYU's overall record since 2002 is 82-46, with 6 seasons over .500. Utah has been to 9 bowls in that time span, with a record of 8-1, including 2 BCS Bowls with a record of 2-0. BYU has been to 7 bowls, with a record of 5-2. BYU has never been to a BCS Bowl. Utah has played 12 teams that were ranked at the time of playing, with a record of 5-7. BYU has played 11 teams that were ranked at time of playing, going 3-8. Since 2003, Utah has played 10 ranked teams with a record of 5-5. BYU did not play a ranked team in 2002, so their record stays the same.
Take this information to mean whatever you would like. For me, the term "Little Brother" comes to mind.
Updated to have the correct Utah record. Not really sure how I did that. Thanks for pointing it out!