The most obvious comparison is that both stories are coming of age stories, one with a boy and one with a girl as narrator. In a coming of age story, a young person discovers something about him or her self that makes him or her grow up. The theme for these two could be: Loss of innocence. A related theme is discovering sexuality and the interaction of boys and girls as they explore sexuality.
In “Doe Hunting” Andy desperately wants to be accepted by the boys and treated as an equal. She shoots and kills a dear, but she thinks she has only wounded it. This experience affects her so deeply that she has a disturbing dream about the deer and when she discovers that she has indeed killed it, it is too much for her. She learns that she does not have it in her to be a hunter. In a way, she is taking a stand.
In “A & P” Sammy is distracted by the girls who come in wearing only bathing suits. He watches them and fantasizes. Then when his boss complains about their lack of clothes, he quits. By quitting he takes a stand in defense of the girls, but he is actually just accepting the difficulty of the adult world.
Both Andy and Sammy learn that growing up is hard, another theme. The world will never be the same for either of them again.
Contrasting the two stories, Andy's experience with the opposite sex is more serious. She is sexually harassed. Sammy does not harass the girls, he stands up for them. These are two very different approaches to interaction between the sexes. However, Sammy does use the girls as his objects of fantasy, which could be interpreted as sexist. Andy seems to show no interest in the boys.