NYC is still plenty dangerous, just not anywhere you've been yet. It's such a different city than San Francisco that it's almost impossible to compare their safety in any general way. But for someone like you, who probably lives and works in Manhattan, you'll likely be more safe than you were in San Francisco. Just don't take this safety for granted or think of it as a joke. NY is a much bigger city than SF and bad stuff happens even in the nicest neighborhoods.

Here's an illuminating map: http://projects.nytimes.com/crime/homicides/map