Border believes the series, which starts in Perth before heading to Melbourne for the Boxing Day Test and concluding in Sydney, is New Zealand's best shot at claiming a series victory in Australia since their only previous success in 1985.

Richard Hadlee and Martin Crowe propelled the Kiwis to a famous 2-1 win over Border's men then and he expects Kane Williamson's in-form side will be just as hard to beat.

"They fly under the radar all the time, they're very good at claiming the underdog tag, but they're not going to get away with it this time because they're ranked No.2 in the world," Border told AAP.

"They were a good team (in '85) and not dissimilar to this team in that they've got some real world-class players but they always undervalue and underrate themselves.

"But they can't just rock up and say 'Oh, we're terrible underdogs, look at this great Australian side' any more.

"They used to say that and get away with it, but now we're behind them.

"Yes, we're playing at home but ... they've just taken care of business (against England) and they're a bloody good, scrapping cricket team."

Tim Paine's side is fifth in the ICC Test rankings heading into the series, but enjoys a hefty home advantage, with New Zealand winning just three of the 31 Tests they've played in Australia.

It took almost superhuman feats from Hadlee, who took a stunning 9-52 in the first innings of the first Test at the Gabba, and Crowe, who plundered 188, to get the visitors off on the right foot in 1985.

Williamson clearly doesn't have that calibre of player at his disposal, but Border says the visitors have the firepower to make life very difficult for the locals.

"I rate them very highly ... they're scrappers," the Fox Cricket analyst said of the Black Caps.

"They're not the superstar-type blokes but they get the job done.

"They hunt as a pack very well ... they're a really good solid unit.

"It definitely is their best chance to win a series since '85 because they've got most bases covered as a team."