The Peloponnesian Wars were really about power. They were fundamentally a contest to decide which power (Athens or Sparta) would be the preeminent power in Greece and the eastern Mediterranean Sea.
The war was due partly to ideological differences between the two powers. Sparta was a monarchy mixed with an oligarchy while Athens was moving towards more of a democracy. The Athenians were generally more interested in culture and individualism.
However, the major cause of the war was power. The Athenians had controlled the eastern Mediterranean because they had a much larger navy. This allowed the military superiority and gave them an advantage in commerce. Sparta (as well as other poleis that were under Athenian domination) wanted to end this and the wars were a result of this desire.