When Moe Green tells Michael that the "Corleone Family don't have that kind of muscle anymore....and they were being chased out of New York by the other families" what did he mean?

I realize the deaths of Luca and Sonny and the war overall weakened the Corleones, but it would also have weakened the other families. The way Moe talks about Barzini makes you think the Corleones were so weak they were about to fold.

I know in the novel there is extensive discussion about Michael wanting the family to look weak, and how he hid the building of the Neri regime even from Tom --- but sticking to the movie, were the Corleones weaker than the other families by this time? I can see maybe weaker than Barzini, but not the others.
Any thoughts?