Compare the father in The Road by Cormac McCarthy to Katniss in The Hunger Games by Suzanne Collins.
This is an interesting question. The most obvious way that the two characters are alike is that both of them get put into harsh conditions--against their will, and most likely caused by human weakness, cruelty and war--in which they have to survive. They did not choose to be in those situations, and in their environments, they have to survive against nature and human brutality. Katniss must fight for her life as others try to kill her, and the father has to do the same, with the added stress of caring for his son along the way. It is a kill or be killed environment that they have to survive in.
Another similarity between these two characters is their fortitude in difficult situations. The father, probably not a brutal or aggressive man by nature, hauls a gun around and uses it and other weapons when he needs to in order to survive. Katniss is the same; it's not like she goes around hunting people for fun on her own time, but when required to, she steps up to the plate. They both demonstrate the ability to survive, using fortitude and strength of character.
They are also both protecting people they care about. The father protects his son, and Katniss protects Rue, and eventually Peeta. This drives them to survive even more; they aren't just doing it for themselves, they are doing it for someone else.
Lastly, they both manage to hold on to their humanity throughout their brutal circumstances. The father could have easily turned to barbarism to provide more meat and protection for himself and his son, but he refused, and even taught his son about "the light" that he should carry within him at all times (humanity). Katniss manages to bring humor, love, compassion and selflessness to the games, something that is rarely seen. Despite her circumstances, she remains human, exemplifying the positive traits rather than the negative.
I hope that those thoughts help a bit; good luck!
Both of these protagonists are motivated to self-sacrifice and action through love of a weaker and more vulnerable family member. In The Road, the Father is driven by love for his son, the Boy. In The Hunger Games, Katniss takes the place of her gentler younger sister, who has been chosen for the brutal fight-to-the-death hunger games.
Both characters function in a brutal dystopic environment, the Father in what appears to be the aftermath of a nuclear holocaust, Katniss in a society in which all but a few fortunate souls live in conditions of exploitation, hunger, and poverty. Both play the hand they are dealt.
Both are pitted against dehumanized humans. The Father must evade desperate fellow wanderers who have turned into cannibals and murderers. Katniss must battle for her life within the context of a decadent, corrupt ruling elite who have more material goods than they know what to do with and find watching other people fight to the death amusing. In The Road, we see the effects on humans of a complete breakdown of the social order and extreme want of basic necessities. In The Hunger Games, we see the effects of too much wealth in making a small group of people cruel. In both cases, the stories are told from the point of view of characters struggling to survive.