Why did the ancient city-state of athens and sparta develop different political systems?

The mountainous topography of the Greek peninsula resulted in the isolation of these two city-states.

Athens developed a system that valued philosophy and active political involvement by its citizens in an early form of democracy. (Note that it wasn't full democracy as we'd think of it today, as those who had a political voice were free men, not women or slaves.)

Sparta developed a militaristic system that valued physical training and military service, as well as a strict loyalty to the state.

a. competition between france and england for land and power