My mum is from New Zealand and I grew up in Australia, but spent plenty of time in NZ as well.
"Better" is hard to define.
People are friendly in both places, but that has changed a lot in recent years in Oz, as more and more people are killing themselves to lead lifestyles they've been led to believe they have to have. Kiwi's are in general a lot more innocent than Aussies in their personalities.
Jobs are shit in NZ and things cost a lot more than you would expect. Prices have jumped a shitload in Oz in the past couple of years too, but the economy still seems to be ticking along. It will crash eventually - it has to - and Australia won't be prepared. A lot of people living in credit in my homeland. Housing is expensive in both places - much harder to find in Oz I think. There is an incredible housing shortage right now. Real estate agents hold auctions for rental properties in my hometown of Melbourne, that's how bad it is.
Yes - Australia has poisonous bitey things that are just waiting to get you. If they don't, the big bastard bitey things will get you instead.
New Zealand has some sheep and large blowflies.
Both countries are stunning. It's often a lot harder to get to see the nice bits in Oz because it's such a big country. New Zealand is a lot more compact.
Women are easy in both places - tend to be a little more princessy and privileged in Oz and uglier in NZ. Both countries have become East Asian melting pots in the last decade - lots of HAPA's in Oz and Asian, Euro, Polynesian mixes in NZ. If you're not happy to accept living with lots of Asian people, the major cities in either country are not for you. Night life is better in the Oz big cities from what Ive seen. International sporting events better in Oz.
I live in Germany now - which has it's own challenges. No killer animals, just lots of rules, regulations and very stiff people who can't laugh.
If I was to choose - I'd pick Australia if I was going to start from scratch and get a job and buy a home. If i was near the end of my working life I'd probably choose NZ.