These are two great stories to compare and contrast given that they both focus on the way that two women experience loneliness and isolation in their society. However, although there are obvious parallels, at the same time we can also identify differences in the treatment of these themes between the stories.
One of the key differences seems to be the way that the protagonists experience isolation and loneliness. In "The Yellow Wallpaper" for example, the narrator is isolated and lonely because of her depression. However, her seclusion is imposed upon her by her husband, who feels that he knows best, and this only serves to make her feel more isolated and lonely. However, in "Miss Brill," the central character is cruelly ignored by an indifferent society, resulting in her loneliness and isolation. A key section to the story is the ending, when having already observed sadly how others must live in rooms like cupboards, we are told where Miss Brill returns to having overheard the nasty comments made about her by the young couple:
But today she passed the baker's by, climbed the stairs, went into the little dark room--her room like a cupboard--and sat down on the red eiderdown.
Miss Brill is forced to realise the way that she is shunned and isolated from an uncaring society. Note the difference though when we compare this to "The Yellow Wallpaper," where the narrator is isolated but with good, if profoundly misguided, intentions.
You also might like to talk about the fantasies that the two characters have as a result of their loneliness. Miss Brill imagines that the whole scene in the park is one important play, with herself as an important character. This of course is a complete fabrication that is designed to give her some sense of self-importance and some value. However, the fantasy of the narrator of "The Yellow Wallpaper" is at least based in fact, as her impressions of a woman trying to escape from the wallpaper are a projection of her own frustrations at being isolated and so lonely:
And she is all the time trying to climb through. But nobody could climb through that pattern--it strangles so; I think that is why it has so many heads.
Note the way that the pattern "strangles," which is a sign of how it traps and restricts, in exactly the same way that the narrator is trapped and restricted.