Yes, both Athens and Sparta had governmental structures that allowed for participation from free adult males, but they differed significantly in their systems and the nature of that participation.
In Athens, the government was a direct democracy, especially during the 5th century BCE. Free male citizens could participate in the Assembly (Ekklesia), where they could speak and vote on laws and policies. They also had the opportunity to serve on the Council of Five Hundred (Boule), which set the agenda for the Assembly and handled the day-to-day affairs of the city. This system encouraged active participation from eligible citizens, though it excluded women, slaves, and foreign residents.
On the other hand, Sparta had a mixed governmental structure that included elements of monarchy, oligarchy, and democracy. The government consisted of two hereditary kings, a council of elders (Gerousia), and an assembly (Apella). Free male citizens known as Spartiates participated in the Apella, where they could vote on proposals put forth by the Gerousia, but their role in governance was more limited compared to that of Athenian citizens. The Spartan system was highly focused on military training and discipline, with a more rigid social structure that placed a greater emphasis on collective responsibilities over individual political power.
In summary, while both city-states involved free adult males in their governments, Athens practiced a more participatory form of democracy, whereas Sparta had a more oligarchic structure with limited participation in comparison.