Growing up in Austin, I remember the big games were always:
OU for national relevance
Arky for SWC relevance
Aggies were rarely in the discussion for SWC glory post WWII until Jackie "FedEx" Sherrill came along. Sure, they would win a championship here or there, but from 1960-the early 80's, it was Texas and Arkansas. If memory serves, from 1960-1984, A&M won maybe 2 conference championships....same as Baylor who was dreadful until Teaff came along. Only Rice, Tech, and TCU won fewer during that period.
The A&M game was interesting and state pride was certainly at stake, but the OU and Arkansas games had much more at stake. Hell, UH was a bigger deal in the late 70's early 80's because they had better teams and were competing for the SWC championship during that period (to say nothing of the 90 UH game)
That was also during the time that not every game was on TV....remember listening to the dulcet tones of the great Ron Franklin during the early 80's on KVET 1300