If by "favourite" you mean "most influential," I'd go with the Luciano organization:
Charlie Luciano broke the power of the "moustache Petes" by eliminating Joe Masseria and Salvatore Maranzano. Though born in Sicily, he was thoroughy modern and American. He formed the Commission as a way of cartelizing underworld activities, and welcomed non-Italians, such as Meyer Lansky, Bugsy Siegel and Longie Zwillman, for what they could bring to the table. Although he stupidly pursued prostitution and drugs (thus setting himself up for bust-and-exile), he had the good sense to appoint Frank Costello as his successor.
Costello (the model for Vito Corleone, imhop) understood the power of political connections, and created a vast network of politicians beholden to him and his associates--he was the guy who "had all the judges in NY." He also continued the alliance with Lansky, and was the only Mafioso to be a partner in an international gambling network that was mostly legit.
Finally, Vincent (the Chin) Gigante, the current family head, distinguished himself by being the only contemporary Mob boss to escape RICO and/or ratting out the other guys. True, he did it by humiliating himself through his non compos mentis act, but at least his family had some continuity in leadership, and stayed relatively strong vs. the other families, which had revolving-door "leadership" and internal strife.