Almost all "rent stabilized" apartments in Manhattan are within spitting distance or throwing distance of market rate. Once a significant number of them cross the $2700/mo threshold in a building, the rent destabilizes.
"Rent controlled" units account for less than 30,000 units in all of NYC. That number is never going up and that number is half of what it was 15 years ago. They are not 4BR apartments for $250 a month. This is a wonderful lie that middle class people believe because they don't actually know anyone with a rent controlled apartment -- they're kind of unicorns in the city.
The rent control board in NYC has approved the maximum increase after every single 2 year freeze since about 1990. Then landlords do improvements to get MCI increases as well. The median rent controlled unit in NYC rents for $1040 and is a studio.
The rent controlled 1BR that I live in has not ever been $250/mo and hasn't been under $1000/mo since maybe 1992.