From Sparknotes.com:
Vito Corleone
The Godfather trilogy presents Vito as the paradigmatic Mafia don. When placed beside him, Barzini lacks class, Don Ciccio looks cruel and petty, and Don Fanucci is smalltime and brutish. Even Michael, despite his tremendous successes, loses in such a comparison, as he appears lacking in warmth and joie de vivre. It is unclear whether we are to believe Sollozzo’s words about Vito, that “the old man [is] slipping,” but even if he is, even if Vito walks right into an assassin’s bullets and survives only though sheer luck, he is still the Godfather par excellence. He is wise and intelligent, an excellent reader of others’ intentions, and a smooth, subtle talker, able to convince with words, not only bullets. The most exceptional thing about Vito, and the way in which he most outshines his son, is the manner in which he conducts his personal life. Though a ruthless, violent criminal, Vito is also a warm, loving father and husband, and the paradox of his character is that it is precisely the warmth of his humanity that makes him appear superhuman. In his later years, Vito comes across as relaxed and playful, even mellow. He has lived a rich, full life and earned a quiet retirement. As a younger man, when he is played by Robert De Niro, he is caring and devoted but also silent and intense. Unlike Michael, he does not let this intensity eat away at him. There is never any tension for Vito between the two meanings of “family” (i.e. blood relations and crime family), and he doesn’t feel conflicted about what he’s doing. Only when he learns that Michael has killed Sollozzo is he noticeably pained. His intensity is that of a hard-working man, though one who still manages to come home at the end of the workday to spend time with his family. In short, Vito comes across as both the perfect father and the perfect Godfather, making him a difficult model for all of his children, especially Michael, to imitate.
Michael Corleone
Michael is cold-blooded, ruthless, smart, and determined. His ability to think clearly under fire, to be decisive, and to command respect makes him an excellent Godfather. Of Vito’s children, he is certainly the best candidate to take over the family. But Michael was never supposed to get involved in the Mafia. He was supposed to become a senator, perhaps even president. Even when he does begin working for his father, he doesn’t seem fully reconciled to the decision. He promises Kay before they marry that the family will become “legitimate” soon. Over twenty years later, in The Godfather Part III, he still seeks this legitimacy. Unlike Vito, who appears at ease in the role of Godfather, Michael is burdened by the responsibility. One senses that he views himself as a sacrificial hero, slaving away for the rest of the family, sacrificing his soul for the well-being of those around him. In many ways, Michael’s story is a familiar one in American mythology: that of the immigrant’s child. He achieves great heights of success, just as his hard-working immigrant parents hoped for him, but at considerable personal cost. In Michael’s case, this cost is to his family life, as he loses his wife and children.
Michael can also be seen as a classical tragic figure. Immensely talented and powerful, he is undone by tragic flaws: his insatiable desire for vengeance, which creates a web of violence and recrimination that he cannot escape; his illusions of omnipotence, which blind him to the fact that achieving legitimacy is impossible; and his sense of being perpetually at war, which never allows him a moment of rest. At the end of Part III, Michael dies alone in the yard of his Sicilian villa. The death of his daughter, Mary, has sealed his fate, severing his ties forever with the rest of the family, the family that he tried to save and bring to legitimacy. Instead, he brought them only pain and death. If Vito is an ideal, almost romantic figure who might make the naïve viewer want to live the gangster life, Michael’s tale has a corrective effect. His life is tragic and his pain immense.