New Zealand might be in good form but they didn't play much test cricket in away condition and last time they went to play against Australia in Australia. They faced a whitewashed, they have a problem of getting choked when playing against Aussie. That's a only reason i gave advantage to Aussie.
For me, if it is NZ vs AUS, then both will be having equal chances. They will be playing in Lord's and both the teams won't have the home advantage. Australia is over-dependent on a few players, such as Steve Smith and Marnus Labuschagne. On the other hand, New Zealand is a well balanced team and they are not dependent on anyone. But then, Australia have players such as Steve Smith, who can win matches in his own. NZ lacks a player of that calibre. That said, I don't want to make any predictions until the India vs England series is over.
If we have Australia vs New Zealand then most chances. Australia will win because even New Zeland is better team but when they are facing mostly they play under pressure which is really bad for them. They need to do some work on better mind set specially against Australia because now they are one of best team in Cricket world and they can achieve any thing they have good leadership good team unit just need to play good against Australia for win.