It's been said, and I forget exactly where, that the Corleone Family was in a decline after the first Godfather movie. However, I don't see any evidence in the second movie that the Corleone Family had lost much of its power. I mean in the book, it says that the Corleone Family established itself as one of the most powerful Mafia families in the country after Michael defeated the Tattaglia and Barzini Families (in the book, he didn't execute the heads of the Five Families).

Of course, the book didn't go as far as the movies so it might not be fair to use it.

Now that I think about it. Perhaps moving out west reduced the power of the family since the big cities had the most influential Mafia families in the country. I don't know. What do you think?