I agree completely with Oli and LW. I’d like to embellish:

In my experience, the most successful people focus on a simple but over-archingly important goal, and maintain focus on it despite every distraction, provocation and temptation. In Vito’s case, I believe his witnessing a two-bit gaboletto having his father, brother and mother killed with a wave of his hand defined his goal: achieving security for himself and his family. Sicilian immigrants were victimized by pezzanovanti, so Vito focused on being a pezzanovante , achieving power to make him their equal—and superior. He became very wealthy, but he never flaunted his wealth: it was a means to an end—power—and power provided him with influence and security. He achieved legitimacy through the respect and devotion he won by providing fellow immigrants with favors and protection. The politicians and judges he bribed gave him power and protection, and many were loyal to him because he kept his word. He knew that he could never be “legitimate” in their world, but he hoped for that in Michael: “,,,Senator Corleone, Governor Corleone…”

Michael was born with a silver gun in his hand. In contrast to Vito, Michael was never focused on a single goal-- he wanted everything at the same time. He wanted to be the top Mafia Don in America—and he wanted to be considered “legitimate” at the same time—it wasn’t a goal, it was an obsession. The key is found in the scene where Michael woos Kay in New Hampshire:

My father's no different than any other powerful man –
(then, after Kay laughs)
-- Any man who's responsible for other people. Like a senator or a president.
KAY
You know how naive you sound?
MICHAEL
Why?
KAY
Senators and presidents don't have men killed...
MICHAEL
Oh -- who's being naïve, Kay?

In other words: Since Senators and Presidents send men to war to be killed fighting America’s enemies, Michael demands to be considered “legitimate” because he has his enemies killed. It was the source of his lifelong frustration: he constantly won battles and lost wars:

He flaunted his enormous wealth with a party for thousands and a big contribution to the State University…but Sen. Geary denounced him as a greaseball and shook him down. He stepped over Fredo…and Fredo betrayed him, nearly getting Kay and him killed. He outsmarted Roth…but never got Roth’s Havana empire. He outfoxed the Senate subcommittee…and lost Kay and his unborn son. He had Fredo killed…and alienated Anthony. He wanted power for power’s sake: He sold the casinos and thought of himself as “out,” but he was never “out”: he was still wanted to be the "Pope" of the Commission. He spent hundreds of millions on the Church to get his Knighthood of St. Sebastian…and Archbishop Gilday betrayed him. Kay called him out for his hypocrisy at his Knighthood party. "I spent my life protecting my family from the horrors of this world," he shouted at her..."But you became my horror," she shot back. He had Gilday and all his other enemies killed...and an assassin hired by Connie’s godfather killed his beloved daughter Mary.

And, as Oli and LW pointed out: he died, alone and heartbroken, in a decrepit Sicilian villa, attended only by a little dog. According to the novel, Vito's last words were, "Life is so beautiful." Not for Michael.