Vito and Michael compare & contrast: why Michael turns out worse
A big motif in this movie is the compare and contrast between Michael and Vito, the two Dons.
Vito was a successful Don. He managed to grow the crime business to its peak, and people liked him. Michael was not a successful Don. The family is in decline at the end of this movie (see Hagen and Pentangli's convo: "The family was like the Roman Empire once, right? ... yeah, once"). Michael is also alienated at the end: he kills his older brother, he has a chilled relationship with his adopted brother Hagen, and he beats his wife and shuts the door on her at the end.
So the question arises as to why Vito was successful whereas Michael was not?
A big contrast is the role of family in both Vito and Michael's lives. We see in the flashbacks that Vito lost his family at a young age and was all alone in Ellis Island when he was 9 years old. We also see how his mother lovingly begged for his life and got herself killed to save him. We can deduce that this experience showed Vito the importance of family. Hence, he himself created a large family, even adopting a non-Italian boy in Hagen. He also doted on his children and grandchildren in the first film; and he seemed to treat his wife well (we don't see much of their relationship, but he does get the rug for her). We can conclude that Vito would have never slapped his wife the way Michael does, and we can conclude that Vito would have never killed his older brother under any circumstances
Michael didn't have the same outlook on family. At the end of Part II, we see, in a flashback, that he joined the army specifically to rebel against the family's control and privilege ("You talked ... about MY future?"; "I never asked for a deferment"). In the opening of the first film, he also hesitates to tell Kay about the family's crime business, such as the story involving "an offer he couldn't refuse"; and he has to insist that he is nothing like his family. The suggestion is that he's ashamed of the family, to some extent. Whereas Vito learned that family is important because he felt the pangs of being without a family, Michael instead had so much family that he wanted to break away from them. Similarly, Vito had a loving mother who died to save him from a wicked crimelord in Italy, but Michael had a family whom he knew as disreputable and criminal. Hence, Michael did not have the same view of family, which leads him to perform actions like beating his wife and killing his brother
Another big contrast is that Vito's criminality has a moral connection. The big example is Don Fanucci. Vito kills Don Fanucci, but when he does so, the audience doesn't feel bad for Don Fanucci. We know that Don Fanucci is a wicked man who exploits innocent storeowners and holds a knife to the actress backstage. When Vito therefore murders Don Fanucci, we feel that Vito is more enacting justice and extinguishing evil. The scene in which he kills the crimelord who murdered his mother is similar. Also, Vito in the first film refuses to get involved with drugs because he feels the product is immoral and would alienate him with his political ties; and he orders only a beatdown of the men who attacked Bonasera's daughter ("We're not murderers, in spite of what this undertaker says).
Vito also saw firsthand that the world had goodness: again, his mother died to save him. A family in Italy hides him from the crimelord and gets him to America. The storeowner was like a father to him when he arrived in America. From these experiences, we can deduce that Vito became a kind man because he experienced the kindess of others in his life . Hence, a lot of the people in the flashbacks seemed to like Vito (e.g. Spinoza wants to give him a rug. the storeowner tries to give Vito a ton of groceries as he leaves). His kindness likely enabled him to make his political contacts too
In contrast, Michael's criminal ties are grounded in revenge, not in triumphing over evil or enacting justice. Michael enters the crime business specifically to kill McCluskey and Barzini in retaliation for their attempt at Vito's life. He gets married in Italy; and his wife, an innocent party, gets brutally killed in a car explosion. His first major act as the don was to murder the heads of the five families. He also had experience with war as a soldier (Santino hints that Michael saw combat). The world for Michael was, therefore, simply far more sinister than the world that Vito experienced. Consequently, Michael turned out more ruthless and cold than Vito, leading him to become alienated from his wife, Hagen, and others. While people liked Vito in the flashbacks, no one apparently likes Michael in the present