I don't know about Wm. Barrett Travis being a hotdog, but he was a hotspur and a dominator, a leader type. As to his successes in battle, he was there when the Alamo was taken form General Cos and 1100 Mexican regulars five months before. Ben Milam was the leader, but he was killed, and Travis and Johnson took over and secured Cos's surrender to a force less than a third the size of the Mexican regiment.
I think Santa Anna's earlier successes had been achieved by Generals Cos and Urrea, usually against militia, whether in Zacatecas or near Goliad. I don't know about his earlier military career in the Spanish army.
Certainly Santa Ana's performance during the US/Mexico war was awful. Legend has it that guys from my home town were the ones who captured his wooden leg after forcing him to make a hasty escape from his campsite. I believe the leg is now in the Ilinois National Guard museum.