Michael did not want to become a man like his father, and wanted nothing to do with the family business, until the fateful hit on Don Vito Corleone, which of course changed his life. Michael then went on to become the head of the Corleone family, but as such, I would argue that he did not become a man like his father.

I think Michael was far more violent and inclined to kill more people than maybe was necessary. For instance, when Woltz tells Hagen he "aint no band leader," they ratchet up the fear a level by killing his horse (and not him) and that does the trick. I also think Michael's tendency to kill several people at a clip was not the Don's style. Even though he was involved in the plans to avenge Sonny's death, I dont know that Vito would have killed more than Barzini, Tataglia, Tessio and Carlo. I think Stracci, Cuneo and Moe Green (with the help of Hyman Roth) would have become very "reasonable" once they realized that the Corleones retained the "muscle" everyone thought they had lost.

Michael also had some of Sonny's temper, which we see flaring up most in GF II in a couple of scenes involving Tom Hagen. One was at the motel in Nevada where he is angry that Tom isnt giving him straight answers about Fredo's whereabouts and Kay's miscarriage," and the other is in the "Take you wife your family and your mistress to Las Vagas" scene. I doubt Vito would have spoken to anyone in his inner circle that harshly in front of others.

Also at the end of their respective lives, they have a world view that is very different. Toward the end Vito,who like Michael, outlived one of his children, and saw the decline of his power, says he makes no apologies for the way he lived his life. He says he never wanted to be a puppet
who danced because someone else was pulling his strings. Mike on the other hand dies alone, embittered, and broken.

Of course the obvious difference betweenthe two men is that Vito is a creature of Europe and Michael is an American. Vito was self made from the streets, and Michael a child of privilege, so they coma at life with different perspectives. Still, I think that at the end, Michael in a perverse way got his wish. He did not become a man like his father.