UK is definitely better for cost of living and salary. Also for choice and quality of products. However, if you're moving to get away from the crime and violence for your family, then somewhere like Christchurch is a good bed. It's pretty safe here compared to UK. The schooling is also good for the kids and you don't need to go privately. Auckland is more like UK.

It's easier to get into NZ than Australia because half of NZ already live in Oz and are still moving over in droves so leaving a vacuum of skills here. The salaries there are high, taxes much lower, cost of living cheaper, lifestyle better, little violence, etc. Many Brits are convinced there are too many bugs and it's too hot. Australia is a continent and it's like comparing Greece to Norway. There is a wide range of climates there. Certainly, if you're coming to NZ for good, consider getting your citizenship and then moving to Oz later if you don't like it here. There are options.

Good luck.