NYC's murder rate of 4 per 100000 tracks closely to the US overall rate of 3.8. There aren't easily sourced stats for Jerusalem, but Israel as a whole has a murder rate of 1.8 per 100000. Unless Jerusalem is exceptionally much worse than the rest of Israel (for which I have no data either way) then I'd have to conclude that Jerusalem is indeed on the same safety level with NYC, or slightly better.
https://en.m.wikipedia.org/wiki/List..._homicide_rate
I have to admit these numbers surprised me.