If there is a linking element between these very different stories, it's probably the sense of loss expressed in them.
Willa Cather presents a scenario in which a woman, the narrator's aunt, returns to a world she loved, from which she's been absent for decades. She had gone from the relatively cultured atmosphere of the American East Coast in the 1860s to live with her husband on the open plain of Nebraska. Her return to Boston and, in particular, the Wagner matinee concert her nephew takes her to are a kind of emotional shock of restoration, but the sense one gets at the end of the story is still one of her regret and perpetual feeling of loss. The last images we're presented with are those of the Nebraska farm she must return to. The background of her early life, symbolized by this concert, is not to be recaptured.
Hemingway's story has a kind of analogy to this because the couple, waiting in a railway station in Spain and ordering drinks at the bar, seem to know that what they had before is lost as well. They converse as if (in spite of the man's evidently trying to get her to agree to having an abortion) everything is all right between them, when in fact nothing is going to be all right. The girl senses that her boyfriend doesn't have the same spark—that her observation about hills looking like white elephants does not mean anything to him, though it would have meant something before, and he would have responded differently. When she tells him to please stop talking, we sense that the reality of their love, whatever it has been, is now ended. Though this is about romantic love, unlike in Cather's story, the fact that in both stories a previous life has been irrevocably superseded is where we can see a parallel between the two works.