Compare Plato and Aristotle on the question of natural inequality. In what sense is the ideal regime one based on inequality? In what sense is this supposed to reflect natural inequality or some other kind of argument for political and social inequality?

Both Plato and Aristotle believed that people are unequal by nature. The main difference is that Aristotle tends to take as a starting point empirical observations about the world as it exists, while Plato begins with a more abstract conception of the nature of the human soul.
In the polis (Greek city-state), one can observe slaves, farmers (the toiling classes), warriors, the wealthy, and a ruling class. Aristotle observes that any city needs all of these types of people and also notes that the skills required for these roles are quite different. He thinks that the innate differences among people are reflected in the division of labor, with the "naturally slavish" most suited to following orders of more magisterial and intelligent owners. Although he considers it unjust for someone who is not a natural slave to be sold into slavery, Aristotle general thinks that the existing social order fairly reflects the capabilities and talents of different sorts of people, and he considers the inequality of wealth and gender inequality natural and fair.
Plato was a far more radical philosopher. He believed that what mattered was not people's external circumstances but the nature of their souls. He thought that all souls partook of the divine and strove to reunite with their divine nature and that different souls were at different stages in their journeys. Thus, different souls were suited to different tasks in an ideal city. Strikingly, he believed that accidents of birth and gender were irrelevant to this, as masculine souls could inhabit female bodies and female souls could inhabit male bodies. His Academy was one of the few institutions of antiquity to admit women and slaves rather than just wealthy young men. His ideal city was strikingly unequal, but roles in it were assigned by individual merit rather than by heredity or convention. Because children were raised communally rather than by parents in the ideal city, the child of a slave might become a philosopher-king and the child of a guardian might become a farmer. Plato was opposed to private property and income inequality, allowing limited amounts of private property for the productive classes and no private property for guardians and the philosopher-rulers. Although people in his ideal city had different roles, they were not divided into the powerless poor and powerful rich.