How did geography affect greek and persian civilizations differently during the classical era?

Greek was a region of mountains.  The region of Greece resulted in independent city-states.  This resulted in the start of wars between the city-states as they were not unified as one.  The nearness to the Mediterranean allowed them to become a dominant power commercially with other regions.

Persia, unlike Greek was unified and had less in-state wars.  The area of the Persian Empire was rather large, and sometimes it became a tough job ruling it.