I live in Christchurch and that's news to me. The central city is best avoided for other reasons: the 2010-2011 earthquakes disproportionately affected the old buildings there and the rebuild means it's a constantly shifting maze of closed roads and detours. This is now hardly noticeable in most of the rest of the city.

I found an article [1] about it which contradicts your understanding of the crime here. Auckland is much worse as a city overall, but Cathedral Square in Christchurch is dangerous compared to the rest of the country. I can't find a good comparison of actual crime rates between countries, but did find articles saying the perception of crime risk is way off here compared to reality.

1. http://www.stuff.co.nz/national/79704084/New-Zealand-rates-f...