There was an astonishing visual display of the battle for the future of New York yesterday in a round-table discussion at City Hall.

On one side: William Bratton, the past and present police commissioner.

On the other side: Al Sharpton, the longtime anti-cop rabble-rouser (and slanderer) who rose to fame and fortune in the 1980s in part by attacking the legitimacy of the Police Department Bratton ran from 1994 to 1995 and runs again now.

In the middle, literally: Bill de Blasio. He got elected in part by expressing his long-held Sharptonite view that the NYPD was engaged in openly racist practices.

But de Blasio’s desire to succeed as mayor led him to select the very same police commissioner who helped inaugurate the aggressive crime-busting and prevention policies that led to the city’s resurrection.

Bratton got the job by agreeing that the department’s “stop-and-frisk” approach had to end.

But Bratton and his boss have made no other visible changes in the department’s approach to crime—and why should they? New York remains the safest major city in America, if not the world.

It’s easy to let things continue entropically when there’s no controversy. Now there is controversy, and the question is inescapable:

Who will have more of a say in running de Blasio’s city, Bratton or Sharpton?

The “round-table” event was staged so that de Blasio could make a public show of his concern about the death of Staten Islander Eric Garner, with Bratton announcing every cop in the 35,000-strong NYPD would undergo retraining.

“Change has been happening, the change will continue to deepen,” de Blasio said. Message: I care.

It was also designed so Bratton could claim the department he recently inherited had been “deficient” in its training efforts, but he was now on the job to change all that.

Well, if de Blasio thought giving Sharpton equal billing with the top cop would pacify his guest, he was sorely mistaken. In Sharpton’s view, the department needs to be changed from top to bottom, to be revolutionized.

According to Sharpton, it is not only stop-and-frisk, but the entire policing approach that had saved New York City from itself, that has to be discarded.

Sharpton effectively pooh-poohed the meaning of de Blasio’s move against stop-and-frisk by saying, in effect, there was no difference between it and the “broken windows” approach of enforcing the laws against small crimes, such as Garner’s illegal sale of cigarettes.

“Given the data that we see in terms of these broken-windows kind of operations, it’s disproportionate in the black and Latino community,” Sharpton claimed, using exactly the same language he and others used about stop-and-frisk.

For example, he said, “If Dante wasn’t your son, he would be a candidate for a chokehold.”

In other words, to Sharpton and others like him, the problem is not lawlessness but law enforcement.

Sharpton said he would not be satisfied with “window-dressing.” Here was his stark warning to the mayor: “If we’re going to just play spin games, I’ll be your worst enemy.”

In fact, New Yorkers benefited unambiguously when City Hall treated Sharpton as though it were his worst enemy. They may smile together now on occasion, but Bratton certainly wasn’t smiling back in 1995 at City Hall, when he stood beside his then-boss, Rudy Giuliani, as Giuliani effectively accused Sharpton of responsibility for a 1994 shooting spree and fire that left seven dead (eight, if you count the murderer).

Sharpton had led a long-standing protest against the owner of Freddy’s Fashion Mart in Harlem, whom he called a “white interloper.”

His inflammatory conduct and that of his deputy Morris Powell certainly helped rile up Roland J. Smith, who shot and killed four people inside the store before setting the fire that killed three more.

The outright contempt with which Giuliani and Bratton (and the commissioners who followed him under Rudy) showed Sharpton were part and parcel of the strong message they were sending about their support for law enforcement and their unwillingness to kowtow to cop-haters and those who profit from social decay and disorder.

Bill de Blasio was with Sharpton then. Will he surrender his mayoralty to Sharpton now?