WFB wrote about his experience with Vidal in 1968 here, (search for "experiencing Gore Vidal") while Vidal responded here.
Reading the 2 Esquire articles (note: WFB sued Vidal for libel) WFB is the clear winner. Vidal article is nothing more than name calling, mostly unsupported or over-the-top, while WFB shows Vidal to be a liar and almost hysterical.
The two men truly did not like each other. WFB never had Vidal on Firing line, didn't want to debate Vidal in 1968 (ABC chose him out of list of 10 possible WFB opponents) and never talked or debated him again in 40 years. From WFB's article it appears they never socialized and their pre-1968 encounters were limited to appearing together once on the David Susskind show and debating at the Republican Convention in 1964.
Further, I can't find a single column or article by WFB on Vidal after 1972 -when the lawsuit was settled. And I've listened to many WFB interviews over the years and whenever Vidal was mentioned he would just utter a mild and very brief dismissive comment (example: "Vidal is not one of my favorite people").