1) I think, "The Godfather" tells a classical tragedy: A young man trying to break away from his criminal family. But it's the good features of his character - his love for the family and his ability to decide quickly - which leads him to a position and a life that he never wanted. He tears out his heart.

2) "The Godfather 2" is artistic in a way that it amplifies the tragedy by showing the parallels of the lives of father and son. One becomes a loved person who builds a family and an empire, the other one loses his family the more he fights for it. It adds to GF2 that it looks beautiful, colorful, rich - Nevada, New York of the 20s, Cuba in the 50s, etc.

3) "The Godfather 3" tries to heighten once more the tragedy: Michael trying to get out, but they pull him back, and in the end he loses what he loved most - his daughter. The problem is: we never really see the love for his daughter, we see Michael as a tired Mafia boss. Why should we feel really moved about his conflict with Immobiliare or with anybody else? It's a gangster movie, alright. But it misses the momentum of the classic tragedy.