Compare the political systems of Ancient Greece and the Persian empire, and factors that can explain the differences and similarities?
Let's try for two of each. We'll start with differences.
1) The first obvious difference between ancient Greece and ancient Persia was sheer size. At its greatest extent, which would have been the Athenian Empire around 440 BCE, the ancient Greek-speaking world would have consisted of perhaps 4 million people, of whom about 2.5 million would have lived in Greece proper. The rest would have lived in Greek colonies or cultures that had adopted Greek language and institutions.
By comparison, the greatest extent of ancient Persia, about 60 years earlier in 500 BCE, the Persian Empire comprised 5,500,000 square kilometers and an estimated 35 million people (see reference.) To put that in modern terms, ancient Persia would be the modern world's 7th largest country, bigger than India, and its 40th most populous, comparable to modern Saudi Arabia. To put it another way, at that time, the world population was roughly 100 million. That is to say, one of every three people alive in the world in 500 BCE was a Persian.
2) Ancient Greece was politically diverse but culturally unified; ancient Persia was politically unified but culturally diverse. Ancient Greece consisted of "poleis," (singular: "polis") city-states with a wide variety of political systems and a constantly shifting structure of alliances and enmities. At the same time, each polis spoke the same language, had similar (though not identical) religious traditions, and shared cultural origins with the rest. The reason for that goes back to point 1, I think: even at its largest Greece was a comparatively small and close-knit culture.
By contrast, Persia was an absolute dictatorship: every part of the empire had the same head of state, the same core laws, and the same bureaucracy to administer them. But again, sheer size made the type of cultural unity exhibited by the Greeks impossible for the Persians. The Persian Empire was divided into satrapies. These were provinces administered by satraps, local governors answerable to the Persian emperor who enforced the law and, above all, collected taxes. From the satrap down, much of life under Persian rule was local. At the risk of excessive simplification, to a degree, if you paid your taxes and did not openly break Persian law, the satrap and his officials did not care much what else you did. That became a fundamental quality of Persian rule. There was certainly a core Persian culture, and many satrapies adopted it. But others, especially those far removed from the cultural center in modern Iran, retained local cultural, political, and social traditions.
Now for the similarities.
1) Both valued sea power. It is a bit hard for Greece to get anything done without sea power: it is a peninsula, stuck to another peninsula, surrounded by islands. In addition, mainland Greece, and particularly the Greek islands, are arid and rocky, making long-term agriculture hard and chancy. Historically, both sea trade and naval warfare have been vital to life in Greece.
The Persians understood the value of sea power too. The first great conflict between Greeks and Persians took place in 547 BCE, when the Persian Emperor Cyrus conquered the Greek colonies of Ionia off the west coast of modern Turkey. Cyrus's goal was to establish Ionia as a Persian stronghold on the Mediterranean. His successor, Cambyses, attacked Egypt to further establish Persian dominance of the sea, and Darius and Xerxes, the two following Persian emperors who fought Greece in the Greco-Persian Wars, were fighting largely for control of the Mediterranean.
2) Both have legacies that extend prominently into the modern world. To begin with, obviously, there are active, thriving Greek and Persian cultures today that trace their history and traditions back to ancient Greece and ancient Persia. Few other ancient cultures can make that claim. Both play crucial roles in the history of foreign cultures as well. The Persian Emperor Cyrus is a significant figure in the Hebrew Bible, and there is a Cyrus Street in modern Jerusalem. The marathon race and even Nike shoes take their names from a Greek story from their war with the Persians. That may be the most important similarity between these two unique societies: in all the vast scope of history, both have proven extraordinarily influential.
There are precious few similarities between the political systems of the two civilizations; in fact they were almost diametrically opposite each other.
The Persian Empire was ruled by a King from a central location; however the size of the Empire was such that he could not effectively rule alone. He employed a number of governors called Satraps to rule in his stead in various provinces. The Satraps were almost always Persian, but he did allow local officials to be chosen from local people with local customs and language. To prevent insurrections or treason, he employed a secret police system known as the "eyes and ears of the King" who provided him with information of events in the far reaches of his Empire.
The Greek poleis were each independent of each other and governed separately. Sparta was most similar to the Persian Empire as it was ruled by two Kings. The Kings were descended from separate families and did not often agree with each other. They could and were often overruled by a ruling council known as the Ephors. Athens was a direct democracy in which all adult male citizens were required to participate in the government. Some other poleis were ruled by monarchs, others by the ruling nobility. Others were ruled by politicians or generals who did not gather power by normal means. They were commonly called "tyrants" because of the method by which they gained power. In almost every instance, the only commonality between the Greek poleis was that the spoke a common language and had a great disdain for all thing foreign. In fact, they often complained that non-Greek persons sounded like the noise of sheep when they spoke: Baa-baa; hence the term "barbarian.
The Persian Empire, as the name suggests, was organized as a unified territory administered through devolved governments. The empire was split into twenty provinces, and each province was presided over by a governor appointed by the king. Ancient Greece, by contrast, was divided into different territories with each having different systems of governance. Some of the territories (such as Macedonia) were established as monarchies, while others (such as Athens) based their system on democratic principles.
One of the main factors resulting in the different political systems was that the Persian Empire was established as a single unified territory, while Ancient Greece was a collection of different territories each with a different administrative system. The Persian Empire was established through conquest, and the political system was inherited from the Assyrians. Persian leadership was personalized by the kings, and despite the territory being vast, the leader maintained ultimate control. The provinces of the Persian Empire were not independent, while Ancient Greece was made up of independent territories.