Senior Green MP Julie Anne Genter is promising to be the "stronger" co-leader if elected to the role alongside James Shaw.
Ms Genter and Marama Davidson went head to head in a Newshub Nation debate on Saturday, ahead of the party-wide vote later this month.
Asked by host Lisa Owen whether the current Green leadership isn't speaking up enough in the coalition arrangement, Ms Genter said she would take a different tack to Mr Shaw.
"James and I have very different styles. He's very collaborative, he's very much seeking agreement and that's great," said Ms Genter.
"I just think stylistically I would be a bit clearer and a bit stronger."
When asked the same question, Ms Davidson said it's important that first-time ministers, like Mr Shaw and Ms Genter, have time to settle into their roles.
"Our ministers need to prioritise their portfolio areas," she said.
"As a non-executive member, [I can] focus on maintaining our independent voice, working with our membership and supporting the portfolio priorities of our ministers."
However, Ms Genter pushed back on any suggestion that her being a minister outside Cabinet was a disadvantage.
"One thing that ministers have, which is a bit of an advantage, is a lot of resources, a lot of support and a huge platform to demonstrate how you're making a difference," she said.
"The [co-leader] position should not be considered on whether someone is a minister or not."
The waka-jumping Bill
The waka-jumping legislation is seen as one of the first tests for the Greens in Government. The Bill from New Zealand First would eject MPs from Parliament if they leave their party.
The Greens have historically opposed similar legislation; however the party failed to highlight its opposition during coalition negotiations, and is now obliged to vote in favour as part of its confidence and supply agreement.
The party voted in support during the Bill's first reading in January. However, Ms Genter said there's no guarantee the Greens will vote it into law without serious changes.
"We need to sit down and have a very frank conversation with our partners in Government and say we have a problem," she said.
"We have to listen to our members, we have to respect our constitution and our policy, and we need to find a way forward [or] we can't guarantee a vote for it at second reading."
Ms Davidson said the entire caucus is to blame for the mistake, but that the focus now needs to be on keeping the party's members informed.
"[We need to make sure] we have regular, transparent, open communications with the membership so they're aware of the sticky issues that are going to come down the line," she said.
Ms Davidson gave the current Labour-New Zealand First-Green governing arrangement an 8/10.
The party's base is still licking its wounds over the handling of Metiria Turei's benefit fraud admission and her subsequent resignation during the campaign.
Ms Davidson was a strong supporter of the former co-leader, but wouldn't say whether she would have Ms Turei back as an MP.
"I think she's done incredible service for our country, [but] we've moved on, the party has moved on and I'm my own woman and am going to bring my own leadership style to this role.
"I want to bring the party together, heal the party and make it clear we have got things to learn from the way it was handled.
"But the point was, and I know this personally, that you should not have to lie or face the choice of getting your power cut off because you do not have enough to survive."
Ms Genter says everyone in the party agrees that the situation should have been handled differently.
"[Metiria Turei] should have been clear about the fact that it's not okay to commit fraud, but it's also not okay to have a system that forces people to lie to survive," she said.
Both Ms Genter and Ms Davidson said there was nothing in their backgrounds that could land them in a similar situation to Ms Turei.
Governing with National
National's new leader Simon Bridges has said his preferred coalition partner heading into the 2020 election would be the Greens. However, both women were sceptical at the suggestion.
Ms Genter said National would have to change a lot of the party's policies.
"Simon Bridges was the biggest cheerleader for increasing oil and gas exploration last term, although he tried to greenwash and say he was investing in public transport, walking and cycling," she said.
Ms Davidson agreed working with a Bridges-led National Government is a long shot.
"[Simon Bridges] opened up Maui dolphins sanctuaries to seismic exploration and mining," she said.
"He would have to understand you cannot pretend to be a champion for the environment while also letting social and economic systems further degrade the environment."