From what I've read on the boards here, the Genovese have always been the most powerful family. Other posters will be able to explain in more details.

I doubt that Paul would or even couldve manipulated Chin. Gigante was extremely shrewed, but also seemed to like Castellano. He was really pissed off when Big Paul was killed and wanted Gotti and all of the conspirators whacked. I doubt anyone could dictate to the Genovese... they're way too powerful and smart.