First off, I understand that the time frame is incredibly generic. I'm talking about anywhere between the Archaic period on through to the Classical.
I've heard a lot about the cultural obsession the Greeks had with competition and drive for glory (ex. the Olympics, Achilles' being a fucking dick 24/7 and being respected for it), but I also read that Greek society, however hierarchy, used pretty fairly egalitarian fighting styles like a phalanx. I think it's egalitarian because there's no troops fighting in some gross trench while some other guy rides around on horseback. Everyone shares a similar role and is expected to work together for collective safety.
How would a glory-hungry Greek soldier reconcile his competitive streak with being ordered to walk closely beside every other soldier?
The reason why there was a change between a drive for personal glory to a drive for equality was because of the rise of the city-state. Basically (I'm generalizing quite a bit), the city-state was founded upon the balance of the upper and lower classes (and thus everyone can be importance) and the devotion of every eligible man to the welfare of the state (with the "eligibility" usually determined by their ability to fight, fighting also granted the right to vote.) Thus, for the first time in the Balkan Peninsula (This would be 9-8th century BCE), the success and power of a state did not rely just upon the upper classes, but also the endeavors of the common people. Because of the rise of such a political system, a peculiar perception of the "model citizen" arose. This model was not based upon self-centered ambitions, but the dedication to the state and its people.
A good way to see this concept is to read the basic story of Cincinnatus of Rome. Though he wasn't a common man, he acted like one (plowing his own fields and such), when Cincinnatus was given great power in a time of crisis, he did everything he could for Rome, stepped down, and promptly started plowing his fields again. No personal ambitions, no greed, no sadistic needs that led to him burning people for candle fires. Just pure, simple devotion to the state, and thus, contribute to its power and stability
(Of course, the balance needed in city-states was largely gone by the approx. 5th century BCE, but it's clear the perception of the model citizen remained the same/very similar.)