A discussion of the theories of society of Plato and Aristotle actually has two components, analysis of how they thought real societies actually operated and how they thought an ideal society should operate. In both cases, they take as a starting point the societies of classical Greece; neither were particularly interested in the societies of "barbarians" (the Greek term for foreigners).
Aristotle divided societies into democracies, oligarchies, and monarchies (either led by hereditary kings or tyrants). He generally accepted social stratification as inevitable, believing that women were naturally inferior and that many people (especially those who were not ethnic Greeks) were "natural slaves". He saw the arts as educating and regulating the emotions and thus having an important role in civic society. His social ideals were just, moderate, and rational. His focus was on maximizing "eudaimonia" (happiness as opposed to momentary pleasure).
Plato was more of an idealist than Aristotle, less concerned with how societies are than how they should be. His main concern was that a society ought to create circumstances which allowed each individual soul to strive towards the divine. He saw education as extremely important. Because of his emphasis on the soul rather than on external circumstances, Plato believed in gender equality; for him, a noble soul might appear in the body of a woman or slave or barbarian, and so his school, the Academy, as well as his ideal society, judged people based entirely on their merits of character and intellect. He generally disapproved of the arts. He disliked democracy because he felt that it selected people for positions on grounds which had nothing to do with ability.