You have a lot of really good material here from which to write, which is where I assume you're going with this. The idea of woman subjugated to man is clear and well documented here. I would only add that both female protagonists have sisters who also try to protect them from their realities; this adds an interesting twist to the purely male dominion idea so prevalent in both works.
Clearly there is ample scope in comparing the position of women in both of these stories, and in particular the way that they are oppressed or subjugated by other males, particularly their husbands, even though their husbands often want to do what they feel is best for them. This leaves both tales open to examination in terms of the issue of patriarchy and how often women are its victims. You might want to explore further the liberty which both women gain, however fleetingly, and compare that to the role that the husbands and males in general play in the story.
You have lots of great points in the above posts, so I will add only this: I have always found it extremely interesting that the one thing which the woman in Wallpaper wants to do (and which now people consider cathartic) is write. She wants to write and create which may have helped her overcome her mental illness, and this one wish is denied her for fear of too much stress on the fragile mental state in which she is perceived.
The woman in Hour is also restricted from doing what she wants which I don't recall if it ever explicitly states what it is that she wants (like the writing in Wallpaper); however, the point is, she is forced to live a life others see as befitting her. Her choices are taken away, and she, too, is trapped and unable to find a healing escape.
In considering the two female characters of Kate Chopin and of Charlotte Perkins Gilman, it is important to consider their ways of dealing with their repression and their perception of freedom. Of course, "The Story of an Hour" is a very short narrative, so this idea is not as well developed; however, there are still suggestions that parallel what is in "The Yellow Wallpaper":
Both stories emphasize the subjugation of the feminine personality in the Victorian setting.
Kate Chopin's use of the pronoun she for several paragraphs is of note, as is Gilman's use of an unnamed narrator.
Both women are alone in their attempts at self-assertion.
In each story, there is another woman who concurs with the "conventional wisdom" of her society. Mrs. Mallard's sister Josephine attempts to shelter Louise from the news and from thinking about her new situation; she calls to Louise through the door: "What are you doing, Louise?" Likewise, the narrator of "The Yellow Wallpaper" has a sister-in-law who concurs with the prescriptions of the doctor and her brother regarding her restrictions.
Both women view the outdoors as freedom.
Louise Mallard looks out the open window and perceives the blue sky, the birds singing--she feels release. The unnamed narrator writes of the gardens outside her room, the flowers, etc.;however, the window is barred for her, so she must look inside the room for release from her repression. This psychological demand for release is found by her envisioning the woman trapped within the wallpaper.
The women find solutions to their repression, but in different ways.
In contrast to Mrs. Mallard, who descends the stairs as "Victory," assuming her environment has changed only to be confronted with her confined patriarchal world, and then weakening again, dying; the narrator of Gilman's story makes an assertive effort to find release. She does so as she frees the woman, although doing so costs her her sanity.
The most intense level of comparison between both is the idea of a woman seeking to define her own narrative. The woman in "The Yellow Wallpaper" wants to write her own destiny... literally. She wants to live her own life in battling what is post- partum depression. She also wants to break free from her husband, his sister, as well as others telling her what to do and how to live. Her desire to keep a diary is a part of this. The idea of wanting to live for self- expression is powerful in the protagonist, something that motivates her to see trapped people in the wallpaper and tear it to shreds. For Louise Mallard, the desire is much the same. She wants to live life away from her husband. This is something that she cannot fully conceive until she hears of her husband's death. While she mourns, she then comes to a realization that with his passing, her own life can be lived. She can order her own dinner at restaurants, she can validate her own voice, or she can write her own narrative. This idea of being the author of one's own destiny is a powerful element in both works. Its denial causes one protagonist to die of the joy that kills and another one to lose her sanity, underscoring its overall importance to both and to all.
Both "Hour" and "Wallpaper" are what we today might categorize feminist works of fiction. Both reveal women who are imprisoned, though one is imprisoned more literally than the other.
The speaker in "Wallpaper" thinks she is on vacation, but she is obviously mistaken. Written to discredit an actual "cure" that the author herself was treated with, the story features a speaker who suffers while being treated with the same cure. The treatment is extremely sexist and demeaning to women. At the heart of the cure is the belief that female mental illness is rooted in the ovaries. It was also believed at the time the story was written that women were incapable of much mental activity, and an excess of such could lead to mental illness. The speaker is a woman trapped in a man's world. She is confined and the victim of a male doctor who also is her husband--she's doomed on both counts.
The female protagonist of "Hour" is also trapped. She, too, is a creative, intelligent woman trapped in a man's world. She is forced to be subservient to her husband. It's not that the man abuses her or treats her exceptionally poor. He doesn't. And that's the point. The world the woman is trapped in is the normal, patriarchal world of her society.
Both stories are drastic in depicting the women's fates, as well. "Wallpaper" features a woman so desperate to escape her situation that she narrates the story in spite of being ordered not to engage in mental activity, and ultimately suffers a breakdown as she identifies herself with the imaginary woman in the wallpaper trying to escape.
When the protagonist of "Hour" finds out her husband is alive, she suffers the heart attack that others in the story worried she would have when she found out her husband was dead.
Both stories deal with the subject of female isolationism. Both are either isolated by family or the situations around them. Both females in the stories desire to either be set free to explore the world on their own terms. One needs to be free from the "shackles" of marriage, and the other needs to be set free from the confines of a man's world.
To look at the stories in comparison one can identify that both of the females lived during the same era. It was a time when women whose husbands had a decent income were expected to be demure and fragile. Women were considered to be delicate creatures that should take to their bed and rest. The husbands controlled the entire destiny of the woman and family. In both stories the women are fragile women who have become psychologically ill due to the pretenses they were expected to demonstrate.
The differences were that one woman is living in the city, her husband has gone off to work, she has a heart condition, and she had believes him dead. The husband appears and she dies because her chance at freedom is lost.
The woman with the yellow wall paper is in a country house on vacation. She is forced to play sick and is told she must rest by her husband and doctor. As a result she descends into madness believing the wall paper has come alive.