What's the MO of Pakistani wickets?
How are they different to the UAE ones if at all they are? Do they have more pace, bounce and movement? If they do, then New Zealand has a much better bowling attack that can take advantage. Their batters too are more accustomed to play in those type of conditions.
And if you're implying that there are absolute flatbed batting paradises , then there's no "home advantage" there too as New Zealand has comfortably the better batting lineup.
And at last if you're implying that they assist spinners a lot more, then we saw how Pak capitulated to Ajaz Patel and Somerville last time around in the UAE so not much hope there as well. And arguably, NZ have better players of spin (Williamson, Taylor, Watling etc) than Pakistan.
Point is....NZ are a much better test team than Pakistan and have all bases covered. So it wouldn't matter where they're playing. Home advantage works when the opposition has glaring weakness in one area (Ban Vs Eng/Aus , SL Vs Aus/RSA) or if the two teams concerned are almost evenly matched (Ind Vs Aus, Eng Vs Ind, Pak Vs SL etc).....
So no. Pakistan wouldn't make New Zealand look anything like Pak in Australia.