The Athenian democracy was unusual in being a direct democracy in which the citizen assembly could vote on laws. Important magistrates were selected by lot rather than elected. As far as the political system went, all adult male citizens were inherently equal (one citizen, one vote), rather than being divided up into orders. The legal system did not have professional advocates acting for people, but rather people had to represent themselves in court and be judged by a jury of their peers.
In the Roman republic, elected magistrates held considerable power and made laws for the people. Like Athens, only adult males could vote, but rather than all citizens being equal, the patricians (aristocrats or senatorial class), equites (knights or rich bourgeois), and plebians had different rights under the law and different roles in government. Freedmen could become full citizens, and women had greater property rights. The legal system was more professionalized, with advocates acting for clients in the courts.
The Romans did not have strict barriers with regards to citizenship, while the Athenians enforced strict limitation to the extension of citizenship. The situation made the Romans build an empire through conquest and extending citizenship to the conquered people. However, this later proved a challenge to the Roman Republic.
Both the Roman Republic and the Athenian Polis were established on a city-state model. However, differences in their geographies saw the states develop in different ways. The Athenians had exclusive cities, which later united through force. Rome, on the other hand, developed on a plain and succeeded in establishing a centralized city-state.
Both the Roman Republic and the Athenian Polis developed well-organized political practices. However, the Romans developed a two-party system consisting of patricians and plebeians, while the Athenians had no political parties.