Labour was also critical of Australian policies such deporting criminals and plans to charge New Zealanders' international student fees.
Ardern said Labour believed National's advocacy had been been weak. "It's one thing as to whether or not you'll walk away with success but it's another issue whether or not the effort was made in the first instance."
She was not underestimating the difficulty, saying since Australia had stripped back the social security rights of New Zealanders in the 2000s there had been little progress in clawing those back. "But that doesn't mean we can't do work on both emphasising that and preventing any further erosion."
She said that was why she had decided to reciprocate if Australian went ahead with plans to charge New Zealanders international student fees - a policy that would triple some fees.
She would not rule out taking a similar approach if further policy changes came up which affected New Zealanders, but did not intend to follow Australia's lead in cutting off wider entitlements for Australians in New Zealand such as social security.
"Rather than diminish those rights, we'll keep arguing there should be equal treatment of those rights."
National Party Foreign Spokesman Gerry Brownlee denied National had been weak in advocating for gains, saying the pathway to citizenship Turnbull agreed to for many working New Zealanders already living in Australia was a significant achievement.
He said the proposed changes to fees for international students were aimed at securing budgetary savings and had also seen fee hikes for Australian students.
He said Labour would not be able to take all the credit if it secured further gains.
"Obviously we would have continued to work to get better arrangements for New Zealanders living in Australia and the current government will do so. If they can achieve more than we've able to so far, you'd see that as part of the continuum of the very strong and positive relationship between the two countries."
Ardern's visit will be fleeting - just four hours on the ground before she returns to New Zealand.
But it ticks off a number of firsts for Ardern - the first overseas trip as Prime Minister and the first motorcade among them.
The brunch is also the entree to the more significant APEC visit next week which will mean discussing issues including the TPP 11 and international security issues including North Korea.
Ardern said she was not worried the relationship would be weaker because she did not have former Prime Minister John Key's close personal ties to Turnbull - or because she was from a left government, rather than conservative.
"I don't think it diminishes the relationship we will have. The strength of any previous relationship I don't think diminishes a relationship in the future, no," Ardern said.
Turnbull could also seek some clarification from Ardern about the future of joint deployments, such as the trainers deployed to Taji in Iraq - a deployment Labour had opposed.
