This is a great question. Let me give you two answers.
First, Sparta did not really put that much emphasis on the importance of building their economy. They were more of a military culture and everything was subsumed underneath this goal. They even created a slave class of people to do their work for them (Helots), so that they could train and create the perfect military society.
Second, Athens was nearly the polar opposite of Sparta. Athens was a wealthy city that sought to obtain every economic benefit. They were poised to do this, partially because they were a naval power. This meant that they would be able to travel the sea for trade and commerce. This fact made Athens wealthy in the ancient world.
In conclusion, Athens cared much more about finances than Sparta and this made all the difference.
Yes, because Sparta spent more money on training soldiers than on economic benefits, whilst Athens constructed Temples (Parthenon) and had huge markets. Alot of Spartian children died of hunger because of the tough training.