Capote started it, slighting her writing ability during a “Tonight Show” appearance. Susann went on later, ridiculing Capote’s voice and mannerisms. Capote struck back by saying Susann looked like “a truck driver in drag.” Susann was going to sue him but her lawyer talked him out of it. Capote claimed that she backed off the suit because her lawyer told her Capote would put a dozen truck drivers in drag and win instantly. Then the lawyer was going to sue, but Capote sort of apologized for putting words in the lawyer’s mouth. This exchange led to Susann including the “Capon” character in her posthumously published novella. Dolores.
All of the above from Gerald Clarke’s Capote biography. While Capote might have been jealous of Susann’s success, it’s also likely that he was just looking to stir up trouble and/or publicity.