As applied to people, both of these words mean "educated," "refined," "interested in and acquainted with what is regarded as superior in learning and the arts." Cultured is considered the more elegant and refined word in this meaning, perhaps because cultivated is more often associated with labor, especially with the output of agricultural products. Nevertheless, a praiseworthy goal for everyone is to be either cultured or cultivated.
Dictionary of problem words and expressions. Harry Shaw. 1975.