Both The Handmaid's Tale and The Road deal with a world in which the society the main characters once knew has disappeared. In both novels, too, a main character is motivated to survive in a hostile, life-threatening world out of love for a child.
However, the two novels have many contrasts. Gilead in The Handmaid's Tale reflects a modern industrial society with all the amenities readers are accustomed to, including ample food, decent housing, indoor plumbing, and good medical care for pregnant women. The main threat to Offred's life comes not from physical want but from any deviation from the rigid rules the new Christian fundamentalist society she lives in have imposed on her. She has to put up with ritual rape and the suppression of any vestige of individualism or personal autonomy. The antagonist in this novel is the warped ideology of the society she has entered and the repression of the human spirit.
In contrast, the man and the boy in The Road face a post-apocalyptic world in which the majority of the human population has been killed in an unnamed disaster that has obliterated civilization. They do not face one culture supplanting another, but civilization itself in ruins. Therefore, the main antagonist the man and the boy face is physical survival: finding enough food, adequate shelter, and safety from marauding bands of survivors who would gladly kill and eat them. Their struggle is far more physically elemental than Offred's.