I have family and friends in NZ and have visited several times and seen the country from the top bit of the north to the bottom bit of the south. It's beautiful and large parts of it are very sparsely populated, so your experience will be dependent on where your DH's job is. In Auckland or Wellington you'll get more of a large town/ small city vibe (nothing like the intensity of London or any major European city) In other parts of the country you could find yourself in a very parochial community where the church is still really important and where your social life will revolve around the children.
It will suit you and your family down to the ground if you are all really outdoorsy, active, sporty people who love nothing more than a weekend cycling, kayaking, sailing or trekking, interspersed with gardening and DIY and taking your kids to rugby training and swimming. If you prefer cultural things — galleries, music, visiting historic houses, grabbing a long weekend in Paris or Rome or Copenhagen — then you'll find it tougher. If you enjoy going to the theatre or musicals or having a night out clubbing then you'll find what's on offer limited. There's some good-amateur level stuff going on but you can forget the West End.
Things like clothes, camping equipment and even books seem expensive. Small population, not as much competition on prices as here. You'll contribute to the cost of healthcare, obviously, which can add up.
My personal take is that there is a lot of ingrained sexism (and obviously it's one of the wokest nations on the planet, and I regard a lot of woke ideology as misogynistic). There's a superficial level of promoting equality but fundamentally this is still a pioneering society and I notice in my extended Kiwi family the boys are all brought up to go to university and into high-paying technical and scientific careers, while the girls are encouraged to go into nursing or teaching.
If you can afford to do it (relocating is very expensive) you might want to go over there for, say three years while the children are young and enjoy an outdoors life with them before working out where you want to settle for the rest of their lives in primary and secondary education. Before you do that, though, find out what your situation would be if you were very unhappy and wanted to go home with the kids, but your DH was intent on staying and fought you for custody. I am aware of a couple of women within my family's extended social circles who came from Europe and the US with their British husbands and appear to be trapped.