Both did very little at ATM and both had success at Bama. Bryant became the greatest coach ever to live and Stallings coached one of the greatest defenses of all time.
Bryant was at A&M at a crucial time. A&M was still all-male, and all military, something which was not that unusual prior to WWII, but which was disappearing everywhere rapidly. It was an incredibly tough job, but Bryant mananged to win. In the course of doing so, he raised expectations. I think that, without Bryant, a lot of Aggies might have dug in their heels and forced A&M into becoming Texas's version of the Citadel. But, football is so important to Texans that Aggies were willing to do whatever it took to compete when Pres. Rudder told them that was what was required, whether it was making ROTC option, desegregating, or admitting women.
Gene's tenure was sort of a victim of timing. Rudder had started to change A&M into a modern university that would be much easier to sell to recruits, but it didn't happen fast enough to save Gene. Had he stayed a few more years, when the NCAA instituted scholarship limitations, and Texas could no longer stockpile recruits just to keep them from competing against the Horns, Gene's tenure might have been different.