The differences were not great - Sparta had a government which was a limited democracy - that is that is it was limited to the adult males who also comprised the army; they met in assembly and made decisions on matters put before them by the council.
Athens started that way but progressively moved to a broader , then a radical democracy (however no women or other slaves need apply).
Both states had executive leadership, but both were constrained by the direct votes of the electorate on important issues.
They became allies when their interests coincided - especially in the face of the Persian threat. Then Athens helped Sparta when part of its territory revolted.
The split began when Athens began to create its empire by manipulating the anti-Persian league formed after the Xerxes invasion was driven off. Athens progressively used the funds for its own benefit and became aggressive throughout the Greek world, which caused a polarisation of city-states behind Athens and Sparta respectively. The split grew and war betwen both blocs ensued (the 27-year Peloponnesian War).
The Spartans won the Peloponnesian war, the only war between the Athenians and the Spartans.
The best war ever
The Spartans and Athens went to war in 431 B.C. and the war ended in 404 B.C.
The Spartans made their own war aims, they did not ask Athens for them.
Alcibiades who defected to the Spartans .
The Peloponnesian War , the war between Athens and Sparta , was won by the Spartans .
Athens and Sparta fought Persia in the Peloponesian War.
I really don't know
Spartans trained for war from early childhood .
Sparta and Athens were allies against Persia in the Persian War.
The Persian empire.Note: Athens was also fighting with the Spartans, see the Pelopponnesian war.
Spartans had a better armty