51,000 new units of housing were approved for development in the City of New York in 2015 which is approximately .6% of the population of the city. That seems pretty low to me.
Unfortunately I can’t find a source for new permits for Atlanta. Anecdotally, I can say that just in my neighborhood in Atlanta has 4000 units slated to come online within the next year, which is .8% of the total population of the city.
I do wish I had more data for both cities for a real comparison, but it does seem like New York City has a housing shortage and there isn’t enough new construction to offset the demand.