I would say the main similarity is in the family structure. Both stories revolve around dysfunctional families with a mother and two daughters. In each case, the mother is hardly a mother figure at all. Katniss’s mother is distant and depressed, but not abusive like Tillie’s mother.
In each case, the protagonist is a girl who is trying to find a way to manage despite family issues. There is a sister in both, but while Prim generally gets along with Katniss, Tillie and Ruth do not get along.
How could I leave Prim, who is the only person in the world I’m certain I love? (ch 2, p. 18)
Another difference is that The Hunger Games focuses on the older sister taking care of the younger one, and Marigolds focuses on the younger sister trying to manage with the complications of the older one’s unstable behavior.