1. Theatricality and drama. Monteverdi is the pioneer of opera as a dramatic fusion of music and text. Caravaggio's paintings are extremely dramatic and even theatrical. The faces are expressive, and never in a conventional way - they are angry, bored, sexually aroused, corrupt, decayed. It is never a passive representation of a scene. It is always brimming with drama.
2. The strange mixture of sacred and profane. Caravaggio used street hoodlums for models when he painted sacred scenes (e.g. The Calling of St. Matthew), and he painted courtesans in a dignified manner. Monteverdi's Poppea ("L'incoronazione di Poppea") is a courtesan lover of Nero, the Roman emperor. The two of them have extremely passionate and sensual duets together, including the tender "'Pur ti miro" at the end of the opera.
3. Music as inspiration. Caravaggio often painted musicians with lutes and other instruments. Monteverdi not only composed opera, but composed opera about music - his L'Orfeo is a piece about the sheer power of music and its impact on the world.
4. Fascination with dark corners of human psyche. Caravaggio obsessed over irrational, wicked, flawed personalities. Monteverdi also puts them in the center of all his major works. Even though he is a half-god, his Orfeo is very flawed and might even be considered weak, as he errs all the time. His Nero is extremely depraved. Even his madrigals couldn't just be simple love songs - they are called "Madrigali guerrieri et amorosi" - "Love and War Madrigals".
