As someone who moved from New Zealand to USA almost ten long years ago it’s difficult for me to give an unbiased answer because I can only really see things from my own little world and thoughts. Of course, some things might have changed since I left.
Depending on where you are now and where in NZ you might be going and what sort of job you do, it’s very likely to be a easy, pleasant move. Living in Auckland suburbia and working at a “normal” sort of job, whatever that might mean, is not dramatically different to living in the US. You would have much the same sort of things in your home that you have now, shop at a similar sort of supermarket and if you ever want to go to McDonalds, Wendys, Burger King, KFC, Dunkin Donuts, Dennys, Pizza Hutt and others, they’re all there too. No WalMart but we have our equivalent called The Warehouse.
There are contrasting / conflicting things about NZ that make it difficult to define. On one hand it might seem like a very socialist place. There are several things that aim towards sharing life’s ups and downs among everyone. We have universal healthcare which is not unusual in the world but some other things are unusual.
In general you cannot sue someone in NZ for personal injury. Everyone pays what is effectively a tax to the government owned Accident Compensation Corporation. If you’re injured at work or elsewhere then you can make a claim to ACC and potentially receive compensation. If a person or company is found to have caused the injury then they could be fined or criminally charged if laws were broken but you still couldn’t sue them like you can in the US.
Social security payment (called superannuation) for retirees is the same amount for everyone. It doesn’t matter what you earned or paid in taxes during your working years. You don’t pay into it separately at all. That’s true of most taxes including healthcare. Tax mostly all goes into one big government bucket. Unemployment benefit is similar. Everyone gets the same amount.
On the other hand NZ is very “capitalist” in that it is strong on free and open markets for business which is the extreme opposite of how we were thirty years ago. I think there are no or very few import tariffs on anything. There are no farm subsidies. Business survives or fails on international merit and competition. There seems to be less rules and restrictions than I hear about here. Anyone can deliver mail, NZ Post does not have a monopoly on mailboxes like USPS does.
Not all business competition has had a positive effect. You can choose to get your electricity from several different power companies but that didn’t seem to lower prices. In my town there were at least four kerbside trash collection companies. You would choose which one by buying different coloured bags at the supermarket. That resulted in four trucks driving down the street looking for just their bags.
Life is kind of simpler and more relaxed in NZ in ways that I find hard to put my finger on. It’s hard to give concrete examples but in general there is a good attitude of live and let live, do what you like, if it’s not affecting me then I don’t care. One silly thing (unimportant, I know) that hit me when I arrived in the US here in summer was not being able to enter a shop or fast food restaurant barefoot. Maybe it’s just me but it honestly never occurred to me that people would object.
I guess this is a New England comparison but the NZ climate is pretty good. It doesn’t get really hot or really cold although it can be humid. It means that a lot of houses don’t have heating. I’ve heard (probably valid) complaints from foreigners that NZ houses are cold in winter. Certainly in the colder climates as you go south they have proper heating.
Some say that there are really two New Zealands. Auckland and the rest of the country. I don’t know much about Wellington and Christchurch but Auckland is much more diverse in it’s culture and population than elsewhere (certainly more than here in New Hampshire). The greater Auckland area has a third of the population so there is good chance you’ll end up there. It’s very spread out and public transport is not great so unless you live and work in the central city, life in Auckland is very dependent on cars. Aucklanders complain a lot about traffic. It is bad but I don’t know that it’s worst than other sizable city. I’d probably still prefer driving in Auckland than Boston.
There’s a perception that property crime is quite high. No way would I leave a house or car unlocked like I’ve noticed people often do here in NH. Although a few tragic cases hit the news, there is not that much violent crime. Gangs are a bit of a problem but they tend to be fighting each other and handguns are almost non-existent. From the news I read, meth, known locally as “P” is a problem. The police in general are highly professional and honest but hopelessly overworked and under resourced. I hear that if your house is broken into and the bad guys have long gone then you probably won’t get an officer to visit. They’ll take the details over the phone or maybe send a civilian employee to take details.
If you have a well paid professional job, you’ll live very well in NZ but you probably won’t earn as much as in the US. The gap between rich and poor in NZ is not as big as in the US but (unfortunately IMO) it is widening. Many consumer products tend to be more expensive than elsewhere.
As for lots of people moving to Australia. Being in a small isolated country makes it quite tempting to want to “escape” and try your luck elsewhere especially when you’re young and want to see bigger cities and countries. Australia is an obvious and easy place to go. Kiwis can freely live and work in Australia without a visa. One of our Prime Ministers long ago had a classic comment on TV about the migration from NZ to Australia at the time. “It raises the average IQ of both countries”. 
The culture is definitely different often in subtle ways that are hard to explain. You should probably visit before you move.
I’m happy to answer questions.
Ross