What are the societal values being promoted in The Canterbury Tales and Piers Plowman and the similarities and differences of these values?
Chaucer's Canterbury Tales are remarkable for (among other things), their use of vernacular. Voices and vocabularies change from character to character depending on the speaker's social standing and education. Though there's some debate about whether Chaucer's position as a court poet made his audience much narrower and more exclusive than the text itself would lead us to believe, many have taken this wide variation in voice as evidence that Chaucer was writing to all; The Canterbury Tales, written in language all could understand, were themselves an egalitarian project.
Unlike Langland's Piers Plowman, which takes religion and the quest for true Christianity as its central theme, Chaucer's stories vary widely and unusually—though religion is a theme, it's by no means the only one. In fact, Chaucer spends very little time describing the pilgrimage itself and focuses instead on the colorful stories of its participants.
Like Langland, however, he does pay particular attention to satirizing corruption, both secular and religious. Though some, like the Second Nun, are models of chastity and goodness, others, like the Pardoner and the Summoner, have been corrupted by greed. Perhaps these themes in both Chaucer's and Langland's works reflect the distance some started to feel between themselves and the Church after the Black Plague ravaged the countryside.
Similarly, both Piers Plowman and The Canterbury Tales observe conflict between social classes. Chaucer observes the conflict both with the stories themselves and their juxtaposition (as a noble knight alternates narration with a humble and bawdy miller). He also examines chivalry and finds it noble but painful (particularly in the tales his own characters in The Canterbury Tales narrate), maybe reflecting social attitudes that were, in his day, pulling away from that long tradition.
Langland's Piers Plowman focuses particularly on the duties and obligations of each class, prioritizing not station in life but rather ability and inclination to behave according to one's duty. He places behavior and action above words (though good deeds may not be all that is required for salvation). Ultimately he approves the quest for salvation, though few other arguments regarding religion and Christian life are conclusive. In later years the text came to be regarded as a subversive one that strongly advocated reforms within the Church and was associated with Lollardy. Whether that was the author's intention is difficult to say.