Sparta took over the south of the Peloponnesian Peninsula and turned the population into serfs who gave half of their produce to Sparta, which supported the Spartan males who were able to divert their life to training as warriors.
Athens had a very rich discovery of silver, and the proceeds were allocated to producing a strong navy, which became the backbone of the naval defence against Persia.
Athens and Sparta.
The city-states of Athens and Sparta joined forces along with the other southern Greek city-states to defeat the Persian invasion in 480-479 BCE, however they were not enemies - they were allies before and after the Persian invasion. Sparta had offered support to Athens against the Persian attack on Athens a decade before that, and Athens supported the Spartans when Messenia revolted against Spartan rule twenty years after the Persian invasion. Not exactly enemies. They became enemies when Athens set out to dominate the Greek world, resulting in the Spartan-led Peloponnesian League and Athens and its new empire clashed in a destructive Peloponnesian War 431-404 BCE. Athens lost, was stripped of its empire and became a second rate power.
Athens converted the Delian League into an empire of its own, and used the forces and money to attempt to dominate the Greek world.
No. An alliance of Greek city-states defeated Persian forces in a series of battles over fifty years 499-449 BCE, led early on by Sparta and later by Athens.
Sparta and Athens were not rivals in 480 BCE - that came more than 30 years afterwards when the threat of Persia subsided. Sparta had promised to help them against the Persian attack on Athens in 490 BCE, but its army had arrived on the battlefield at Marathon too late. They remained on good terms and were natural allies in the Persian invasion in 480-479 BCE, providing the two largest contingents to the southern Greek coalition, led by Sparta, which repelled the invasion. Even if Athens had not been friendly with Sparta, it had no choice because it was a prime target of the Persian invasion and needed all the help it could get. It was not a case of Athens joining force with Sparta, it was Athens seeking the help of Sparta and its allies. They remained close allies for another 20 years, Athens helping Sparta put down a rebellion in its territory. They fell out when Athens started interfering in the affairs of the Peloponnesian League cities (which Sparta led) and Athens ignored Sparta's appeal to back off, leading to an all-out war.
Allies Sparta and Athens had a falling out when the Spartan helots revolted and the forces Athens sent to help Sparta began to side with the revolutionaries, and Sparta sent them home. Athens turned the Delian league it had led against the Persian Empire into an empire of its own, and began to interfere in the cities of the Peloponnesian league led by Athens resulting in open war.
Sparta and Athens were at various times allies and adversaries. The main clash was the Peloponnesian War 431-404 BCE when the Spartan Peloponnesian League fought Athens and its empire in a devastating war whic embroiled the Greek world from Sicily through to ASavesia Minor.
Because the Persian army wanted to destroy individual Greek poli, so Athens convinced other poli to combine forces with them and make a league or an alliance in order to attack the Persian army and eventually win.
Sparta had the best military forces, enough to take out Athens.
They each provided major forces for a coalition of southern Greek city-states to resist the Persian invasion. After the invasion was repelled, Sparta left the follow-up action to Athens. They remained allies until Athens converted the anti-Persian alliance into an empire of its own after the Persians gave up trying to enforce peace in the western Mediterranean. Athens over-reached itself and this led to the Peloponnesian War between a Spartan alliance and Athens and its empire. In this war Persia gave assistance to Sparta to help it defeat Athens.
Sparta led the Peloponnesian League, which opposed the intrusions of the empire which Athens had formed out of the anti-Persian Delian League. The Peloponnesian War started in 431 BCE, paused in 423 BCE then resumed until Athens and its empire were defeated in 404 BCE.
Athens and Sparta both had very efficient fighting forces and and were the two powerhouse cities in Greece.