I have relatives in NY, and they would disagree with that statement. NJ does fare better in this version than in the originally proposed bill (you are correct there).
But CA is going to get creamed, because a greater portion of their deduction is from state and local taxes that rely less on property taxes than does NY and NJ.
Other than Long Island and Westchester. A $500,000 home in NYC is around $4k in property taxes. The family living in that home would probably pay $7k-$10k in local including me tax plus state tax. Upstate property taxes are real low from what I’ve seen.