Compare and contrast "The Wife of Bath's Tale" and Sir Gawain and the Green Knight

Since the other Educator does a great job contrasting the two works, I will focus on the similarities between the two.
While the “Wife of Bath’s Tale” was written after the era of medieval chivalric romance, the narrative contained within is itself an example of that genre—or at least a parody of it. The knight in this story comes to understand the importance of honor and trust when he finally decides to accept his wife despite her outward appearance.
Similarly, Sir Gawain learns the importance of honor after accepting the sash he believes will protect him against death. The Green Knight forces Gawain to admit his cowardice and apologize for it, but he does this only because strengthening Gawain’s honor and trust was the entire point of the Christmas game to begin with.
Each story features a doubting knight who seems unhappy with an aspect of his destiny before finally coming to accept it. With that acceptance, both knights are rewarded: the ugly wife becomes beautiful, and Gawain gets to live after all.

"The Wife of Bath's Tale" is a late middle-ages tale that explores the role of women in an English society. It seeks to challenge the existing notion that women were only to play a subordinate role to men in the society. On the other hand, “Sir Gawain and the Green Knight?” is a tale from the same period that emphasizes the need for people from various gender and social classes to stick to their traditional roles since it brought prosperity, both to the individuals and the society at large.
The most common thing between the two tales is that they explore the English life during the late 14th century before the coming of the renaissance where society underwent significant change. Both stories acknowledge that rules and customs governing different groups of people contributed to both individual and societal success. In the case of "The Wife of Bath's Tale" story, the author emphasizes that a constant evaluation of traditional roles is required to maintain a just and cohesive society. In the case of “Sir Gawain and the Green Knight?” it is argued that sticking to traditional societal roles leads to prosperity.
The main difference in the two stories is the approach they take towards the role of women in society. In "The Wife of Bath's Tale," it is argued that women should be given more sovereignty over their lives to the point of gaining equal social status as their male counterparts. In “Sir Gawain and the Green Knight?” tale, chivalry romance is promoted and the traditional role of women in society is not questioned.

"The Wife of Bath" is a story within the greater work of The Canterbury Tales by Geoffrey Chaucer. Chaucer was an educated court cleric in London and lived between 1345 and 1400. His collection of stories is considered seminal in the English language because it is a record of the East Midlands dialect used in London during the Middle Ages, the primary ancestor of common English today. It is also celebrated as an early example of diverse, innovative creative writing in the English language. 
Written during the same era, Sir Gawain and the Green Knight is of unknown authorship and originates from the area around North Derbyshire, geographically and culturally distinct from London then, as it is now. 
The content of these two works reflects the differences in the two cultures of the era. The Canterbury Tales is a story of pilgrims of myriad social classes mixing and mingling on a shared holiday. The Wife of Bath's story, particularly, questions the role of women in society and how they exert power in relation to their male counterparts. Sir Gawain and the Green Knight, is a story of classic chivalry, opening in King Arthur's Court itself.
Though concurrently created, The Canterbury Tales looks ahead to the social changes of the Renaissance, while Sir Gawain and the Green Knight celebrates the heraldry of the medieval past.