There were glorious and meager times for both.
The political power of Athens rose to its peak after the Persian Wars when the Athenians founded the Delian League. It was then, that Athens became the leading power in the Greek world. After the defeat in the Peloponnesian War that followed some decades later, the Athenians never gained this role again (although-always arrogant-they never admitted it).
On the other hand, the Spartans, a leading political power in Peloponnese from the archaic period, became the absolute power after the Peloponnesian War…for a while. Exhausted and corrupted, they, too, were soon left behind, as the Thebans initially and the Macedonians afterward took the lead.
Is the impression that Athens thrived, and Sparta withered a false one, then?
Not exactly! The social and production structure of Athens permitted a quick recovery in her finances and always remained, even in the Roman period, one of the capital cities in culture. Sparta, on the other hand, had never invested in culture and the release of the helots from the Thebans was a big stab in her finance. Once politically down, they never recovered in any way.