Those three are still generally considered the most prestigious public HS in NYC.
Some might add Hunter and Townsend Harris. But Hunter, while public, isn't run by the NYC school system, but by the CUNY school system. Hunter might have the lowest admission rates of all.
This older NY Times article shows a 1.7% acceptance rate at Hunter. Probably lower nowadays. That's significantly lower than the acceptance rate for Harvard or any U.S. university.
https://www.nytimes.com/2017/03/10/n...ions-rate.html
Then there are a bunch of newer, smaller public high schools with very good reputations, but they aren't as well known yet as the traditional big three.
Also hard to make apples-apples comparisons bc they have differing admissions requirements, and the applicant pool differs across schools. The big three tend to be very heavily Asian and from Brooklyn/Queens, and the smaller schools tend to be more white and Manhattan/Brownstone Brooklyn.