it comes after years of mediocre or bad play coupled with the rise of that program's rival.

Roger Reid and Steve Cleveland were let go after bad seasons, but during that same time the Utes were going deep into the NCAA tourney with Fat Rick and Ray Giacoletti.
Gary Crowton was fired after three losing seasons and a rape scandal, but during the same time Utah went to the Fiesta Bowl and had their first outright conference championship since the Eisenhower administration.

Jim Fassel was let go after the '89 season. BYU finished the season ranked and beat Utah that year 70-31.
Ron McBride was let go in 2002. This was a bit of an anomaly since BYU had a terrible season in 2002 too. But in 2001, BYU was 12-2 and finished the season ranked and you could make the case that entering into the 2002 season, BYU was ranked and trending upward while Utah was going nowhere. McBride was on the hot seat entering into the '02 season and his 5-6 record that year sealed his fate (even though he beat BYU).
Ray Giacoletti was fired after two consecutive losing seasons and finishing 6th in the Mountain West. During the same time, Dave Rose had righted the ship and BYU won the regular season conference championship and went to the NCAA tourney.
Jim Boylen was also fired after two consecutive losing seasons. During that same time, Jimmermania was in full swing and BYU went to the Sweet Sixteen.

With Utah's invitation and recent success in the PAC-12, the utes are trending upward while BYU is losing traction amongst fans. It makes sense to make a coaching change now to take the program in a different (better) direction.