Strength build is more about teamwork and the ability to end fights quickly so that the round ends quickly/prevent long drawn out duels.
Agi is more about dictating where the fight happens and trying to outskill the other person in a 1v1 duel.
I'm not saying that agi is solely that of a rambo or str is solely that of a teamplayer, but in a team battle local superiority is easier to obtain if your team can one hit everyone and wittle down the enemy by half in 5 seconds, as well as having a high survivability.
However, at Strategus level battles, agi and str need to work together in order to win. Personally, i believe that ath should be important for support toons like shielders, archers, pikeman. But for the shock troops, the base in which these support group operates, str is the best.