When approaching the assignment of comparing and contrasting short stories which do not immediately appear to have more than slight similarities or differences, the best approach is to find one commonality between the two and put one's focus upon it. In doing so, the writer can, then, evaluate the different approaches that the two stories take toward this commonality, establishing similarities and differences with them. So, with reference to the short stories by Kate Chopin and Eudora Welty, one commonality is that the existence of the two female characters, Louise Mallard and Phoenix depends upon their being "alive."
As way of explanation, the writer can examine what Welty wrote in her essay "Is Phoenix Jackson's Grandson Really Dead?" She responds to this frequently asked question about her story:
....his being dead can't increase the truth of the story, can't affect it one way or the other. I think I signal this, because the end of the story has been reached before old Phoenix gets home again: she simply starts back. To the question...I could reply that it doesn't make any difference. I could also say that I did not make him up in order to let him play a trick on Phoenix. But, my best answer could be, "Phoenix is alive."
Phoenix has a purpose to life; therefore, she is "alive" and perseveres in her existence, which has been given meaning. Thus, for Phoenix, the "worn path" is existential; it is what gives meaning to her life, it is her raison d'etre [reason for being]. Now, in the case of Louise Mallard, until her husband under whom she lives a repressed life dies, she has no true raison d'etre. Bentley Mallard's death--in contrast to the life of the grandson--is what (but also, all that) affords Mrs. Mallard the freedom to live. This realization, expressed in Louise's "Free, free, free!" underscores this idea. As long as Louise Mallard has this freedom, then, she, too, "lives." But, when it is stolen from her by the reappearance of her husband, she dies of "joy that kills." In contrast, Phoenix's freedom does not depend as much upon the life of her grandson; it exists in her traversing of the "worn path." Existential meaning, "aliveness" for both women depends upon their sense of purpose. Married to Bentley, Louise has none, but on her own she has "freedom" and purpose; on the other hand, it is the path, the journey, in which she feels alive that affords Phoenix her purpose.
For convenience, there is a link on how to write a comparison/contrast essay. The writer will want to remember that the introduction includes a "hook" or motivating thought that captures the reader's interest. Perhaps, then, including Welty's line that Phoenix is alive can be worked into this introduction. Then, the thesis statement will follow which establishes the similarities and differences that the writer will discuss.