Often, a book-a movie, or an album is greater than the sum of it's parts. However, in the case of the Hunger Games Trilogy (HGT), I'd argue that the book's greatest influences are comparable (in the case of Twilight) or far better (Spartacus and 1984).
Why the Twilight parallel? Well, both series feature a heroine in a love triangle. Now, on one side you have a clutzy, damsel in distress who has to choose between a werewolf and a vampire. HGT has a kick-grass archer (Katniss) who chooses between a dreamy (he's a day-dreamer) baker or a handsome hunter who helped Katniss learn how to provide for her family.
Okay, but Spartacus? Well, Spartacus was the most famous slave leader in a major slave uprising against the Roman Empire in 80 BC or so. In HGT, Katniss leads a revolution against a totalitarian empire* called "The Capitol" of 13 states* The citizens of the Capitol all have Roman names.
Last but not least, is George Orwell's 1984-the book that originated the phrase "Big Brother Government." In both books, the individual is the subordinate to the state and not the other way around.
Anyway, literature isn't an island, in most books, the influences are noticeable. The idea however is to take those influences and create a seamless work of his/her own. Unfortunately, the "Hunger Games Trilogy" comes off as pretty clunky and inferior to other books in it's genre(Sci-Fi) which it's trying to emulate. That being said, the trilogy is addicting, and gets people reading-which is great.
Compared to "Twilight," though, "The Hunger Games Trilogy," is the better series. But, that's kind of like saying that the University of Utah Football program is better than BYU's Football program this year. Although both are lucrative and have huge fan bases, you can't deny the mediocrity of both.
"The Hunger Games Trilogy," however, can be compared to the Harry Potter series, which is a compliment. Both series of books are gateways for young readers into other more mature books of their genre. The Twilight Series however, are a gateway into, well, Harlequin books maybe? Supernatural Jack Weyland?
*Yes, there's a US history parallel.