I suppose that both played a role in their respective falls from grace. Salieri allowed his own sense of jealously and envy to reach unmanageable proportions. In his own search to appropriate the world in accordance to his own subjectivity, Salieri must bear some level of culpability in not exercising checks and limitations over this self destructive element. Through his depiction in the play, Mozart's responsibility for his own predicament lies in not understanding that talent does not guarantee happiness. While Mozart was brilliant in his talent, he did not fully understand that there is a pragmatic dimension to living in the modern setting where talent does not guarantee a complete sense of contentment.
In Peter Shaffer's Amadeus, Mozart has the God-given genius but none of the emotional or political savvy to be successful. A former child prodigy, he behaves, well, like a child still. He makes crude jokes, mocks the court, flirts with all the ladies, and pouts when not given his way. Mainly, though, he is haunted by his father. He knows that he owes much of his talents to his father, but he seems never to live up to his unwieldy expectations. Whereas his father and Salieri measure success by public and material show, Mozart measures it inwardly and artistically--the way God intends. In this way, Mozart works himself to death, trying to please his father instead of his heavenly father or himself.
Salieri is Mozart's foil in every way. He has none of the talent, but all of the political cunning. An overachiever, Salieri suffers from morbid jealousy, a need for spiritual revenge, and an intense inferiority complex. He curses God for giving Mozart all of the talent; more, he curses Mozart for taking all his talent for granted. A two-faced hypocrite, Salieri befriends Mozart, only to destroy him. He uses women and Mozart's memory of his father to drive the prodigy to bankruptcy, near madness, and death.