New Orleans is far more dangerous than New York. About 12x higher homicide rate than New York on a per person basis. It’s actually the most dangerous city in the country now: https://www.fox8live.com/2022/12/29/new-orleans-homicide-total-climbs-highest-26-years/?outputType=amp
New York is actually quite safe. Most Americans are just put off by how dirty it is relative to other cities.
That said, there’s a big geographic divide. Other than French Quarter, I’d stick to places that have an A-, A, or A+ grade here: https://www.niche.com/places-to-live/new-orleans-orleans-la/
Or I’d wait a few years until the city government starts taking crime seriously after tourism numbers crater. When I visited in 2018, the homicide rate was 38 per 100k. Last year it was 70 per 100k.