This question deserves a two-fold answer: While "Leper" Lepellier demonstrates maturity through his experience in the war and his reflection upon it, Gene is the one who truly comes to a new and more mature understanding by the end of this novel.
He goes from being an alienated, introverted newcomer to being a campus "regular," whose understanding of others has progressed from cynical pessimism to near-adult comprehension of human diversity and its effects on behavior.
While the main characters in A Separate Peace all demonstrate maturity, the reader should see the most maturity in Gene. Gene begins as an insecure outsider, jealous of those who seem to assimilate so well into the Devon culture. By the end of the novel, he realizes (through Finny's example) that not everyone has selfish or ulterior motives.