There are certainly some notable similarities as well as differences between the two stories.
1) Setting: Both stories are set in New Orleans. This is significant, as the placage system of biracial common-law marriages became chiefly associated with New Orleans during the 19th century.
2) Plot: Both stories raise similar themes. The fate of the quadroon woman and her difficult assimilation into polite society remain the chief concerns in both works. It's important to note that the placage system only received superficial acceptance during the 19th century. While Southerners largely tried to ignore what they considered a necessary evil, Northerners viewed placage as sexual slavery. In both stories, the female protagonists are viewed as figures of curiosity and suspicion. From here, we can discuss the tragic quadroon figure in Southern literature.
3) The tragic quadroon: In the exposition to Tite Poulette, Madame John is characterized as a former concubine who has experienced great suffering in life. Both Madame John and her daughter, Tite Poulette, are prime subjects for local gossip. Before Monsieur John passed away, he bequeathed a house to his beloved concubine for her use. However, Madame John unwisely sold the property and afterwards, deposited the proceeds of her gains at a bank (which later failed). Now, mother and daughter must survive on the wages Madame John earns as a dancer at the Salle de Conde.
This background information characterizes the quadroon as a tragic figure to be pitied; she belongs neither to the white nor to the black communities. The tragic quadroon is often portrayed as a woman who must endure the same kinds of racial prejudices her darker-skinned peers are subjected to. Rather than being safeguards, her white skin and fragile beauty are curses. She is simultaneously sought after by men and rejected by society. If she is bereft of a protector at all, her position in society becomes tenuous and her future, uncertain. Similarly, "The Little Convent Girl" addresses the plight of the quadroon who elicits sympathy but simultaneously excites wary speculation about her identity.
4) Emasculation: In both stories, the father is an absent figure and the masculine influence is rendered ineffectual. Here, you can provide brief examples from both stories to support this statement. Also, a question worth pondering: is Kristian Koppig an emasculated figure?
1) Major differences lie in the climax and denouement of both stories. While the climactic moment in "The Little Convent Girl" involves the convent girl's fateful meeting with her African-American mother, the climactic scene in Tite Poulette involves Kristian Koppig asking for Tite Poulette's hand in marriage and her subsequent refusal.
In "The Little Convent Girl," readers discover the convent girl's quadroon identity when she meets her mother. However, the conflict is not yet resolved at this point (some may characterize this as a false climax that foreshadows a devastating denouement). The underlying conflict remains unresolved despite the girl's reunion with her estranged mother: indeed, the question of her integration into New Orleans society still has to be addressed. The author's denouement is shockingly effective: the convent girl commits suicide; it is her answer to the racial predicament she finds herself in.
In Tite Poulette, however, the denouement comes with an answer to Tite Poulette's problem. Tite Poulette's mother relinquishes her own maternal connection to her daughter and proclaims Tite Poulette the Spaniard's daughter, clearing the way for Tite Poulette to legally marry Kristian Koppig. Yet, there is a rich irony here: Madame John's maternal sacrifice clears the way for Tite Poulette to marry, but it does not ultimately change Tite Poulette's biracial heritage. The two opposing denouements highlight the quadroon woman's precarious situation as well as the stark choices she must face in the battle to reclaim her social significance.
2) The diasporic condition: While Tite Poulette hints at the African diaspora that made the placage system possible, there is no such indication in "The Little Convent Girl." You can use descriptions of the quadroon balls in Tite Poulette to begin the discussion of how they are connected to the African diaspora.
Hope this helps!