I've mentioned before, the book contains parallel experiences for Vito and Michael:

Michael, in the hospital: "For the first time since it had all started he felt furious anger rising in him, a cold hatred for his father's enemies."
Vito, after accosted by Fanucci: "But at that time all he felt was an icy rage that this man planned to rob him of the money he had risked his life and freedom to earn."

I think that feeling of cold anger or rage is the call to "one destiny" for both men. The book, though, contains multiple hints that Michael is essentially the second coming of his father, and I don't think the movie is necessarily committed to that notion .