In a sense, the two works are very different, with Hawthorne's being a serious literary work exploring the religious and philosophical themes of outer versus inner beauty and the other being a piece of mass culture.
In Hawthorne, the point of the woman's disfigurement is to contrast her inner beauty and goodness with her husband, who can only appreciate outward and superficial beauty. Like many of Hawthorne's characters, the heroine of The Birthmark symbolizes a point about the corruption of the fallen world that can only recognize the superficial values of outward conformity, virtue, or beauty, as opposed to true Christianity in which "the letter killeth but the spirit giveth life."
The audiences of The Hunger Games also value external beauty more than inner values of loyalty and love. The heroine's exploitation of these, and modern society's valorization of women as decorative objects (would the film have been a hit had the lead actress been fat and worn glasses?) show how patriarchy has been internalized by women.
Well to me these things are the main topic of many popular literature because that is what our modern society is interested in.