Not necessarily. The Genovese were still strong in certain rackets that the Gambinos never were involved in, including the Teamsters and casino gambling(Vegas, the Carribean, Europe). The Genovese, through guys like Jimmy Blue Eyes, Trigger Mike, and Patsy Erra were still the strongest family in South Florida. They had Morris Levy in the music industry. They had the Lee Morris agency in Hollywood. They just didn't have the one big out front boss that they had had previously, which made sense because the previous big bosses, Luciano, Costello, and Genovese, had been hounded relentlessly and had either deported, forced out, or died in jail. Chicago, the Genovese, and Gambinos were on equal footing at that time, Carlo Gambino was just the most recogizable boss at that time.