The statement that best explains the differences between the democracy of the Athenian polis and the structure of the Roman Republic is:
"The senate of the Roman Republic was composed of wealthy patrician magistrates whereas the Athenian ecclesia and Council of 500 were made up of various citizens drawn by lot from different territories within Athens."
This statement accurately highlights the contrasting social structures and mechanisms of governance in both political systems. The Roman Senate was primarily composed of aristocrats (patricians), while Athenian democracy allowed for broader representation of the citizenry through random selection.