The NYC crime rate varies wildly by neighborhood so I don't think its very useful to compare city-wide crime stats. For example, the felony assault rate is literally 10x higher in parts of the Bronx than on the UES. If you live and work in safer neighborhoods the city will appear to be very safe to you.
In NYC the most dangerous areas are pretty far out from (edit: downtown) Manhattan and you'd really have to go out of your way to get there. Anecdotally I lived in Chelsea and worked in Union Square for a few years and never witnessed any real crime, violent or otherwise. By comparison I also lived in SF where the bad parts are unavoidably located in the center of the city and I've witnessed multiple violent crimes over a similar time period. The neighborhoods in a city you pass through on a day to day basis really matter in terms of defining your experience.
In NYC the most dangerous areas are pretty far out from (edit: downtown) Manhattan and you'd really have to go out of your way to get there. Anecdotally I lived in Chelsea and worked in Union Square for a few years and never witnessed any real crime, violent or otherwise. By comparison I also lived in SF where the bad parts are unavoidably located in the center of the city and I've witnessed multiple violent crimes over a similar time period. The neighborhoods in a city you pass through on a day to day basis really matter in terms of defining your experience.
Check out this map for stats: https://maps.nyc.gov/crime/