I'm not an expert and happy to take corrections from other people who are better informed but this is my understanding.
So the fundamental difference is how Britain colonised the two. When they landed in Australia, the Brits could not find evidence of any permanent buildings, which according to their thinking meant the land was unclaimed. 'Terra Nullis' was the policy they used. Now that may have been somewhat true, Australia is a huge country and many Aboriginal people were nomadic and moved between different areas but it's not as though the British scaled the entire country before they made that call. And according to the policy of Terra Nullis - they could basically move in and start setting up. Relations between Aboriginal people and white settlers deteriorated, disease wiped out an inconveivable number of their population, and massacres and genocidal policies against the Aboriginal people started to ramp up. Today, Australia's most vicious racism is usually towards Aboriginal and Torres Strait Islander people. Not sure if it's still available on SBS on Demand but the First Australians documentary is worth a watch.
Now the Maori people of New Zealand did have permanent settlements and were not considered Terra Nullis. I know much less about the specifics of their history but I understand that by the time serious conflicts broke out between Maori people and white settlers, they had been living alongside each other for decades and both sides had access to European weapons. And that placed both groups on more even footing to fight and negotiate.
To give an example of how that translates today: the All Blacks (NZ rugby team) do the haka (a Maori cultural dance) before they play but an Aboriginal AFL player (Goodes) was ostracised for pointing out general and specific racism he was experiencing as a football player. Maori culture seems to be much more integrated into every day life in New Zealand. To the point where I've never even been there and know a couple of Maori words. I don't know any words from Aboriginal languages.