NATO is an intergovernmental military alliance led by the United States during the Cold War
No city won. The Sparta alliance with Persian backing defeated the Athens alliance or empire.
Athens converted the alliance it led into an empire of its own.
The Persian Empire and an alliance of Greek city-states led first by Sparta and then Athens.
Afterwards, Athens converted the alliance it had led in the latter stages into an empire of its own, and used and misused those resources, leading to the peloponnesian War against the alliance led by Sparta, which devastated the Greek world.
Sparta led the Peloponnesian League, Athens led the Delian League.
The war was not a contest for control of Greece, it was between the Athenian alliance/empire and the Spartan-led Peloponnesian alliance. Athens was taking its power too far and the Peloponnesian League drew a line in the san which Athens ignored, bringing on the war.
Athens was part of an alliance of Greek city-states which varied in size from a couple of dozen to 180, led at first by Sparta, then later by Athens after defeat of the Persian invasion.
The Athenian empire was stronger at sea, the alliance led by Sparta was stronger on land.
There were several alliance during the fifty-year war. One side was the Persian Empire. The other was varying coalitions of Greek city-states - first the Ionian League 499-493 led by Miletus, then a southern Greek coalition 480-479 led by Sparta, and then the Delian League 478-449 led by Athens.
The war between Athens and Sparta was the Peloponnesian War. the ancient Greeks called it the war between Athens and its allies and Sparta and its allies. The word Peloponnesian was used because the alliance led by Sparta against the Athenian empire was the Peloponnesian alliance, as most of the cities were in the Peloponnese Peninsula.
As Greeks, their cultures were very similar. Their alliance was for self interest - Sparta aided Athens, and Athens reciprocated.