If you mean Sparta and Athens, they were not rivals but supported each other. The rivalry came after the Persian invasion was repelled and Athens turned the Delian League it had led against the Persian Empire into an empire of its own and used its resources to try to dominate the Greek world.
There were scores of armies - those of the Greek city-states in Asia Minor which revolted against Persian rule. They lost after a six year struggle.
In 499 BCE the Ionian-Greek city-states in Asia Minor revolted against Persian rule. Over the next six years the Persians progressively defeated them and restored control.
Athens and Sparta.
They adopted a superior strategy of first defeating the Persian navy, and cutting off their sea supply line. The Persians had to send half their army home for the winter, and the Greeks united the city-state armies to defeat the depleted Persian army.
The Persian Wars covered 499 to 449 BCE in several phases. The invasion of mainland Greece was 480-479 BCE.
Zoroastrianism was the dominant religion practiced in the Persian Empire. It was founded by the prophet Zoroaster and emphasized concepts of duality between good and evil, free will, and the worship of one supreme deity, Ahura Mazda.
Athens led 180 eastern Greek city-states against the Persians in the last 30 years of the 50-year Persian War.
United Arab Emirates
they formed the delian league because they had to join toegether to defeat the Persians
Restoration Prior to Israel (Judea) returning to its earlier state of being a sovereign nation it was ruled by Persia, after the destruction of Solomon's Temple. This time of rule was called the Persian period.
It allowed it to convert the Delian League which it led against the Persian Empire into an empire of its own and live high on the hog on the proceeds.
That could be United Arab Emirates.
The Persians had used their usual preliminary of bribery - their emissaries had been through the Greek city-states offering bribes to the aristocracies to accept Persian rule within which they would retain of their own city-state. It worked with the northern ones, but the southern ones resisted.
Neither - they both left Greece in a state of undecided warfare, still fighting the Persians, and still fighting each other.
The Judeans did not defeat Persia, the Persians under their king Cyrus the Great took control of Judah which was already under control of the Babylonians whom Persia replaced as ruler. The Babylonians had already deported the entire aristocracy of Judea. Persian king Cyrus the Great allowed them to return and try to reclaim their ancestral estates.