I would go with "to size up", because the expression "se medían" conveys the idea of comparing themselves to each other in a competitive way, to boost their egos (and I'm not criticizing, ha ha ha, I'm just saying, that's how it goes and that's how those games are played). So "to size up" is a good translation.
You could also say "in the 13th century they measured (or judged) themselves by how good they did in the tournaments, afterwards, in the 20th century, they did it with dogfights" or "they measured themselves by how good they were in the cockpit of an airplane" or something like that...