USC has 3 Heisman's in that period. Ohio State is the only school that has one of each in that period. Texas has two Naismith's and got robbed of a Heisman.
Really, the only schools that have had decent sustained basketball and football success over that period are OU, Texas, Michigan State, Ohio State and Florida. Michigan State tends to play a grind it out style of ball on both fronts that is not conducive to producing the stats to win national awards.