Your milage may vary. I live in Auckland, retain a presence in Wellington and feel ridiculously safe in both.
I lived, stayed and travelled all over the USA and felt a lot less safe there by comparison with NZ, UK, Canada and Australia. South Africa on the other hand was off the scale dangerous.
We have our issues, as all locations do, but it's a marvelous existence, and a great place to consider for start-ups.
