This is a great question! There are lots of ways that you can compare and contrast the two central protagonists in these texts, Mrs. Mallard and Nora. However, the wording of your question seems to identify the central way that you can explore their presentation. Both characters are oppressed females in a patriarchal world full of patriarchal institutions, especially marriage, that force them to become something that they are not. Likewise, both characters experience liberation through the action of the story, although in the case of Mrs. Mallard, this liberty is short-lived. Both reveal that the patriarchal institution of marriage has the potential to squash and inhibit the growth, maturity and development of a female from occurring along natural lines, as the wife has to meet a whole host of societal expectations to fulfil her "role" as wife.
Therefore, if you are writing an essay on this topic, I would explore the nature of the word "oppression" as applied in this case and the way that both characters reveal. Then I would consider how Nora and Mrs. Mallard gain liberation. Hopefully the points I have given you above will give you lots of ideas for what you can talk about. Good luck!