Why Greece???

The advantage the Greeks, and later the Macedonians, enjoyed was largely discipline. Additionally, the Greek hoplites (heavy infantry, roughly), were better protected by large shields, and in many cases, body armor. Above all else, however, good discipline saved Greek armies from disaster, and offered good prospects of victory when the Persians could not keep their troops in hand, and did not outnumber the Greeks in overwhelming numbers. In all wars, from ancient times up to the present, troops have their best chance of survival when they maintain their cohesion as units, and support one another; and the face the greatest prospect of destruction when their organization breaks down. Once a formation breaks down, and loses its cohesion, the former military formation becomes a mob, and a mob of panicked individuals. An attacker usually pays a high price initially--but if successful, can inflict even greater casualties on the defender.

There were Persian troops (the Immortals) who were a match for the Greeks in discipline. The Persian Shahinshah ("King of Kings") was loathe to commit them to battle, however, as they were also his Life Guard, and maintained him on his throne against challengers and rebellion. The colonies of Asia Minor (equals the modern west coast of Turkey) had rebelled, and the Athenians had come to their assistance. It was for this reason that Darius originally decided upon an invasion of Greece.

Even when the Immortals stood to a Greek attack, they were not as well provided with armor. This could be a disadvantage, though, for the Greeks, because body armor and shields that cover the soldier from nose to ankles are heavy--they can't spend long in the line fighting without becoming fatigued. Usually, the Greeks were victorious soon enough to drive off their enemies, even when they lost.

Just before 400 BCE, Cyrus, the brother of Ataxerxes, the Persian emperor, rebelled against his master, and hired Greek mercenaries to march out to challenge his brother for the throne. At Cunaxa, near modern Baghdad, he defeated his brother's army, largely thanks to the Greeks, who held together when just about everyone else, on both sides of the battle line, were losing their heads (figuratively and literally). Cyrus, however, was killed. The leaders of the Greek troops (called "the Ten Thousand," although there probably weren't ten thousand left by then) went to negotiate with the Persians, and were betrayed and murdered. Thereafter, younger men who had acted as officers took command and the Greeks marched north, eventually reaching the Black Sea, along the southern shore of which they then marched west to return to their homes. One of those young officers was Xenophon, and his Anabasis is a classic of ancient literature, telling of the expedition, and of how the Greeks, so long as they kept their discipline and followed orders, were able to cut their way out, and march back to their homes, although it took almost two years from the time they had first signed up with Cyrus.

Same thing with the Romans. Discipline and a rational organization can produce armies which mediocre men can lead to victory over military geniuses.