Err, no. All spartiates (IE: spartan citizens) were comparatively wealthy. (It gets a bit tricky due to the way spartans owned and managed their wealth) you had to afford the big honking armour in order to be a spartiate in the first place.
And yes, athenians had slaves, but athenian citizenship was significantly broader than spartan citizenship (Athenian citizens made up something like 1/3-1/5 of the population of Athens (it varied over time), Spartiates only a few % of the total population of the spartan state.
Sparta was an oligarchy based on the land-owning elite. (because you need a certain amount of wealth to afford hoplite armour) Athens was a democracy based on the navy (because a rower does not need much in the way of equipment)