These are two excellent short stories, though arguably there are different and perhaps more pertinent ways to compare them. Examining the protagonists through the theme of choice seems to highlight differences rather than similarities. In "Hills Like White Elephants," for example, it becomes clearer and clearer that Jig is not really given a choice by her partner. The way that he keeps on refering to the abortion, bringing it up again and again, even after she asks him to stop it, indicates very clearly that he wants her to have an abortion and that he will leave her if she does not. Note one of these exchanges, towards the end of the tale:
"But I don't want you to," he said, "I don't care anything about it."
"I'll scream," the girl said.
Jig is forced to threaten her partner with public embarrassment through making a scene in order to get him to be quiet about his insistence, disguised as indifference, about his desire for her to get an abortion. Throughout the story, Jig's lack of choice becomes more and more evident.
By contrast, in "Cathedral," we can see that the protagonist, in spite of his initial reluctance and unwillingness to engage with Robert, chooses more and more to allow himself to be led through an experience that triggers an epiphany in his life as he experiences something of Robert's blindness and finds that his perspective is curiously enlarged as a result as he draws and Robert's hand remains on top of his:
So we kept on with it. His fingers rode my fingers as my hand went over the paper. It was like nothing else in my life up to now.
The narrator of "Cathedral" chooses to engage more and more with Robert, and finds that he himself benefits from this relationship. This is very different from the position of Jig, who is given a choice that appears to be no choice at all.