Fahrenheit 451, Ray Bradbury's cautionary tale about censorship, is one of the most celebrated and studied dystopian tales ever written. It has been the basis for a great deal of imitation and reflection. It concerns a world where the printed word is considered subversive and must be destroyed.
The Hunger Games, by Suzanne Collins, is a recent work of dystopian fiction about a world in which a powerful state Government controls all the work and resources of twelve districts, keeping the common people living in poverty under strict law. Every year, the Government stages the Hunger Games, where two children from each district enter a huge arena all together and fight to the death.
Both works deal with possible future societies, and both take a negative view of the power and control Government takes over the individual. In Bradbury's work, the Government keeps its people under control through deliberate ignorance; they cannot have printed material and so cannot read classics or learn from history, or write new books, and without anything to learn from the society is lawless and hedonistic. Collins's work has a similar Government control structure, but hers is more brutal; the Government simply keeps its citizens poor and desperate, working like slaves with no chance of escape or advancement while the rulers in Government live like kings off their work.
Fahrenheit 451 is more concerned with the idea of intellectual knowledge and the ability of books and words to change people, both in their thinking and their morality. The protagonist's friends in the firehouse have no regard for either human life or property; they see their work as sanctioned by the Government and so above all judgement. The Hunger Games is more concerned with the brutality that a centralized, state-controlled world will necessarily commit on its citizens to keep them under control; the Games themselves serve as a warning to citizens that no one, not even children, are safe from Government retribution.
The works have other similarities and differences, most notably semantic differences like tense and audience, but they are most similar in what they say about the evils of an all-powerful Government structure, with no concern for the rights of the individual, where all production, commerce, and activity are intended for the support and comfort of the Government structure itself instead of for the workers who produce and create.