Compare and contrast Katharina and Bianca in The Taming of the Shrew.
The two sisters are of course used as foils for each other throughout this Shakespearian comedy. Katharina is presented as the "shrew" of the title, who is depicted as a woman who is constantly wrangling with either her father or any potential suitors that come. Other characters again and again describe her as someone who is always in a bad mood. Note how Hortensio refers to her after feeling the sharper side of her tongue in Act I scene i:
From all such devils, good Lord deliver us!
However, what is interesting about her character is that she is not in any sense a flat stereotypical character. She shows herself to be a fully-developed person who clearly is a fitting subject for the sympathy of the audience. This is established through the crass treatment she receives from the unimpressive series of suitors in Padua, the way that her father clearly prefers her younger sister and his overall view of marriage as a way of gaining wealth. Any audience can appreciate the wit of what she says, indicating her intelligence that other characters are not able to handle. Note too, however, that she is shown as a character who is able to care for others. For example, she protects the servants from her new husband's whims and anger.
Bianca in contrast is described as someone who is attractive, being the character quite a few male characters are said to be in love with. Her looks are able to snare Lucentio at his first glimpse of her. Clearly, when compared to her sister, Bianca must appear incredibly tempting as a character who is submissive and modest. However, it is clear that in spite of this appearance that Bianca cultivates, she reveals a somewhat darker side, clearly showing her selfishness to her sister and her resentment at the way that Katharina's reputation is a barrier to her receiving all the attentions that her many suitors would like to give her. Note how this anger reveals itself quite openly when Bianca is slapped by Katharina when she suggests her elder sister must be jealous of her.
Of course, one of the major comparisons you need to make between the two sisters is what happens in the final scene with Petruchio's "competition." Katharina's promptness in responding to her husband's call in comparison with the tardiness of Bianca shows that there are different rules in operation depending on the marriage. Bianca has now married Lucentio and so she obviously feels she does not have to obey him any more and can use her marriage to indulge her selfish desires, whereas Katharina shows that she takes her role seriously.
In addition to the other very good answer to this question, it helps to think of Katharina as something of a "proto-feminist" character. Katharina, for example, is often a character who appears to exhibit feminist philosophy, as she refuses to marry the suitors of Padua and also seems to rebel against the concept that women are goods exchanged between men in marriage. This idea would have been revolutionary in Shakespeare's day, but its revolutionary effect is tempered by the fact that, in the end, Katharina is "tamed," meaning that she submits to her husband's will, and this action is presented as an epitome of wifely devotion. Thus, though Katharina is a fascinating study as an early feminist character, any feminist critique of the play needs to grapple with its less than feminist ending.
Bianca, on the other hand, doesn't really exhibit the same feminist characteristics that make Katharina such a fascinating and complex character. Bianca is mostly presented as a good-willed and pretty young woman that essentially exists to be pursued by men. As the other answer suggests, Bianca's submissive nature is complicated at the end when she appears to be a more strong-willed wife than would have been expected. Though this action can be seen as something of a feminist rejection of male authority, Katharina still has the strongest feminist side of the sisters. Of course, this is only one interpretation. All in all, comparing and contrasting Bianca and Katharina as feminist characters is a fascinating project, and certainly a productive way of thinking about the relationship between the two characters.