Final answer:
The Palazzo Rucellai and the Palazzo Medici differ in their architectural styles and the representation of their patron's families, with the former reflecting early Renaissance humanism and the latter the power of the Medici family.
Step-by-step explanation:
A crucial difference between the Palazzo Rucellai and the Palazzo Medici lies in the architectural design and the personality of the families that built them. The Palazzo Rucellai, designed by Leon Battista Alberti between 1446 and 1451, became a prototype of early Renaissance architecture, explicitly utilizing the classical ordering of columns and proportional relationships in its design that reflected the principles of Humanism. Contrastingly, the Palazzo Medici, with its more robust and fortified aesthetic, does not showcase the light and clarity characteristic of Alberti's work but is more indicative of the Medici family's power and influence in Florence, sporting notable features like the Medici Chapel and the use of allegorical family representations in frescoes, as seen in the works by Benozzo Gozzoli.