What gave archosaurs the edge as large predators at this time, and therapsids the edge as smaller ones? Frankly, I am not sure. Both seem to have had heightened metabolic rates and fur or feather insulation... Perhaps the chief advantage enjoyed by thecodonts centered around their big, slashing attack jaws. These may have made them better big-game hunters, while the more precise cutting teeth of therapsids were more suitable for smaller prey.
Gregory S. Paul (1988) Predatory Dinosaurs of the World, Simon and Schuster, p. 53