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.