Unfortunately I see a number of issues with your chosen essay title. Whilst I think it would be perfect for an analysis of "A Rose for Emily" and an examination of the character of Miss Emily and what drives her to the rather drastic lengths she takes to secure herself a husband, dead or alive, I can't see how the title can equally be applied to "Miss Brill." Miss Brill is not a character that has ever known the possibility of romance as far as we know it. There is no information in this tremendous short story to suggest such a relationship in the past. Indeed, part of what makes this tale so poignant is the desperate loneliness that she suffers and the way that she is forced to eavesdrop into the lives of others to gain entertainment and a sense of being alive. Note what the text tells us about her:
They did not speak. This was disappointing, for Miss Brill always looked forward to the conversation. She had become really quite expert, she thought, at listening as though she didn't listen, at sitting in other people's lives just for a minute while they talked round her.
We get the sense as readers of this short story that Miss Brill is only able to enjoy life as a spectator sport, rather than living it herself, compared to Miss Emily, who at least has some experience of love and life.
Therefore, if you are going to compare and contrast these two texts, you will want to think about and consider the profound isolation that both central characters suffer. Both Miss Brill and Miss Emily are definitely isolated from the worlds in which they live, but for very different reasons. I would select a thesis statement like the following:
Miss Emily and Miss Brill are both isolated figures in their worlds, but for radically different reasons.
This would allow you to establish the shared theme of isolation whilst also giving you scope to talk about the differences. Good luck!