Sparta and Athens had very different governments. Sparta was a militaristic state. This means that all decisions made by the government revolved around the wants and needs of the military. This resulted in Sparta developing one of the strongest armies in the world during this era.
Athens on the other hand had a form of democracy. A democracy is when individual citizens have a say in what laws are made and what representatives there are in the government. This gave the average Athenian much more political power in comparison to Sparta.