None.
Basically, it's a discussion club or debating society where bishops discuss the meaning of church documents. The USCCB seems to have been modelled on the DNC, the ADA, or the ACLU. It's a kangaroo court dog&pony circus with buffet dining. Aside from the photo-ops and the quiche, it has little if anything to do with Catholicism.
Under Bernardin and during the '80s (Reagan era), there was some political flexing for cameras on nukes and socialist pieties, half in nostalgia for Vietnam-era social protest. The sodomy scandals have sort of quieted things down. No serious Catholic takes the USCCB seriously. It has about as much to do with the Catholic faith as the DNC.
John Paul II does. He has devolved authority in certain areas to the national bishops conferences (Friday abstinence, observance of certain Holy Days on Sundays, communion in the hand, and other liturgical matters). Of course, no episcopal conference can bind an individual bishop, but they do tend to express consensus through those conferences.