What does western sport have that compares? Gold medals for your country?
I think it's a mistake to evaluate sport by only looking at the very highest level. Almost nobody competes there, and in professional sports, I'm not sure that's always where you would find the best role models either :-)
Also, I think you have touched on 3 different things - military training, martial arts training, and sport. (The MAs that we practice today are no longer military, in general - IMO - although they may have that in their heritage somewhere.)
I believe that classing these pursuits as "higher" and "lower" is misleading.
I don't believe any of them necessarily make you a better (or worse) person, although they all have that potential.