Briggs is very hostile towards Harry's methods of getting investigations done whether illegally or otherwise with threats or intimidation, because he felt Harry's extreme methods were damaging the public image of the San Francisco police department.
Following the death of Threlkis from a heart attack (which Harry instigated by bringing up how Threlkis had Joan Doaker killed), Briggs scolded Harry for ruining months of surveillance & intelligence work. He also brought up Special Investigations had been working overtime into building a case against Threlkis. When Harry said, "maybe we saved the taxpayers a little money", Briggs continued to scold Harry by threatening to bust him down to the Traffic department or kick him out of the police force altogether & also felt Harry's ways of doing things don't fit in a new era. When Harry called him out on the hypocrisy of murderers getting away with killing people, Briggs contined to sneeringly scold him: "Hey, don't you lecture me you son of a bitch. You know who you're talking to, huh? You know MY record ?" (in reference to Briggs' accomplishments in the police department, having been there longer than Harry). Getting angry, Harry responded, "Yeah. You're a legend in your own mind!" Briggs angrily said, "Goddamn you, Callahan!"
After the Police Commissioner & Lt. Donnelly suggested that Harry should go on vacation in order to prevent furhter retaliation from Threlkis' mafia organization, Briggs noddingly approved that Harry should be on vacation. Briggs then said, "Think things over, Callahan. Get with it. It's a whole new ball game these days," to which Harry countered (as he was leaving the Police Commissioner's office): "Funny. I never thought of it as a game."