Seeing Australia's performance against India, I don't think Australia will be able to win a series if a series will be held between Australia and New Zealand. The New Zealand team is stable enough now. They are playing very well. So I think both teams will have equal chances to win the series. Players make a lot of mistakes on the ground. The players of the team who make fewer mistakes, they will win. Because both teams have enough talented players.
You cannot conclude like that, India beat Australia in their last tour as well and everyone thought New Zealand would do the same but the result were entirely different as Australia dominated New Zealand in the three Test matches and you cannot compare how a team could perform because they saw the last series.
Look at the way India was over shadowed completely by England in the first Test match and no one thought consider how India played in Australia with a depleted team.