The greatest difference between the Persians and the Greeks was undoubtedly in form of government. Persia was governed by a king, who was a quasi-divine figure. Moreover, he unified Persia, a huge and diverse empire. The Greeks were very different.
The Greeks did not have a divine king that governed all of them. In fact, by the time of Aristotle, the Greeks had 1,100 independent cities. This means that each city ruled themselves. This is a radical difference. Moreover, these cities had various forms of government - tyrannies, democracies, oligarchies, and even mixed constitutions like Sparta. For example, Sparta had two kings, five ephors, and a council, called the gerouisa. All of this is in stark contrast to Persian.
Finally, I should mention that during the classical era, the Greeks did not really like the idea of a king.