Fanboys and critics are cruel about the work of directors, but evidently not so cruel as other directors are -- if Flavorwire's collection of the 30 nastiest director-on-director insults is any indication. (Hat tip, Anne Thompson). Even the supremely unflappable Clint Eastwood flips one to Spike Lee.
My favorite take-down is Jean-Luc Godard's of Quentin Tarantino: "Tarantino named his production company [Band of Outsiders] after one of my films. He'd have done better to give me some money."
Also amusing is the serve-and-return between Tim Burton and Kevin Smith. After Smith tweaked Burton for stealing the ending of Planet of the Apes from a Smith comic book, Burton snorted, "Anyone who knows me knows I would never read a comic book. I would especially never read anything created by Kevin Smith." To this, Smith retorted, "Which, to me, explains [effing] Batman."
Filmmakers work in their own bubbles. Unless they are close friends, they typically encounter other filmmakers in the supercharged atmospheres of film festivals and awards shows where tension and competition are high.
Many of these Mean Boys provocations are collected by journalists at film festivals where one publicity-seeking filmmaker gets ink by dissing another. Hence Spike Lee, upon release of his World War II-themed Miracle of St. Anna, bashed the paucity of African-American soldiers in Eastwood's Flags of Our Fathers, eliciting the elder filmmaker's retort: "A guy like him should shut his face."

I'll shut my face. Heard any other good directorial takedowns?