NCAA tournament appearances:
Utah - 26 times (5th most in NCAA history)
BYU - 24 times
Sweet 16 appearances:
Utah - 15 times
BYU - 6 times
Elite 8 appearances:
Utah - 5 times
BYU - 3 times
Final 4 appearances:
Utah - 4 times
BYU - Never (they do hold the record for most appearances without a final 4, so you have Utah beat there)
National Champions:
Utah - 1 time
BYU - Never
Season ending in the top 25:
Utah - 20 times
BYU - Couldn't find it, but I would guarantee it's far less than that
Conference Champions:
Utah - 36 times
BYU - 30 times
Conference Tournament Champions:
Utah - 5 times
BYU - 3 times