It remanined a dominant military power in both wars - it commanded at sea and on land in the Persian war, and led the Peloponnesian League to victory over the Athenian empire in the Peloponnesian War.
Its ongoing problem was declining manpower - the accumulated casualies it took in wars meant that the force it could deploy progressively shrank until it could no longer maintain dominance.
Were you talking about the Greek Persian and Peloponnesian Wars? If so, the Persian war was between the invading Persians and the defending Greeks, who formed a league in which the military was led by one of the Spartan kings. (Sparta had two kings at the same time.) In the Peloponnesian War, it was the Delian League (Athens and allies) vs. the Peloponnesian League (Sparta and allies) Sparta ended up beating Athens after destroying their fleet.
Athens and its empire versus the Peloponnesian League led by Sparta.
Sparta led a coalition of Peloponnesian city-states which we today call the Peloponnesian League. It was already in existence before the Persian Wars - comprising the Dorian city-states of southern Greece.
Persian War - the Persian Empire versus varying coalitions of Greek city-states. Peloponnesian War - the Athenian Empire versus the Peloponnesian League led by Sparta.
Persian War: The Greek cities of Asia Minor provided a third of the Persian navy for the 480 invasion of southern Greece. The Greek city states of central Greece provided a substantial part of the Persian army which fought the southern Greek armies. Peloponnesian War: Athens and the cities in its empire fought the mainly Peloponnesian cities led by Sparta.
Persia had the money to bankroll the Spartan-led Peloponnesian League to build and man a fleet which could compete with the hitherto dominant Athenian fleet.
Sparta remained a dominant military power until later wars erode its strength to the stage where Thebes defeated Sparta and took over dominance.became the dominant
The Peloponnesian War was between Athens and Sparta. It was after the great Persian war, when Athens and Sparta worked together to defeat Persia. The Peloponnesian War was started because Sparta feared Athens may dominate them one day. There was a big battle between them, lasting for many years, but in the end, Sparta won.
Sparta and Athens joined 20-odd other Greek city-states to oppose Persia. After that war,the Peloponnesian League led by Sparta fought the Peloponnesian War against the Athenian empire.
After the Persian invasion was repelled, Sparta left the ongoing wars and turned its attention to controlling revolts by its large serf population. It headed the Peloponnesian League which came into conflict with Athens after the Persian war was over and Athens turned the Delian League it had led into the war into an empire of its own. This conflict led to the Peloponnesian War in which Athens was defeated and Sparta became the dominant power in the Greek world for the next 30 years, when the constant wars amongst the Greek city-states so weakened Sparta that it was displaced by Thebes, and faded out of power.
Persian War: a coalition of the southern Greek city-states versus an expeditionary force from Persia with its local Greek allies. Peloponnesian War: the Athenian league/empire versus a mainly Peloponnesian League led by Sparta.
If you mean the bond they had after the Persian war when they both were in the Peloponnesian League (or, at that point, Hellenic League), no. Sparta withdrew from the alliance and re-created the Peloponnesian League with its old allies. Athens led the Delian League. The two leagues fought in the Peloponnesian War.