I know people advise against using overseas phones in NZ because of frequency issues but I got the above phone new for US$160 so it was hard to resist given it's 64GB RAM and running the Qualcomm 835 which is fairly decent.

Took a bit of work to unlock it from Sprint (not for the faint hearted for sure since it meant using fastboot first to remove the SIM restrictions and then flashing a stock Sprint ROM) but now it's working fine on Vodafone.

The only issue of course are frequency bands. The phone supports the following LTE bands

As can be seen from that the only LTE band the phone has that is used in NZ is Band 3. LIving in Wellington I get LTE most of the time and occasionally H+.

On a recent trip up north the phone would drop to 3G but the speed seemed to be okay for general surfing etc (didn't try to watch videos) so I actually wondered in the indicator on the display was correct?

I suspect it would be better in Australia since from I can tell the following bands are used

Australia is currently using these LTE bands
2100Mhz (B1) – Telstra (a handful of sites), Optus (Tasmania), Vodafone
1800Mhz (B3) – Telstra, Optus, Vodafone
850Mhz (B5) – Vodafone 
2600Mhz (B7) – Telstra, Optus
900Mhz (B8) – Telstra (a handful of sites, utilises spectrum previously used by 2G)
700Mhz (B28) – Telstra, Optus 
2300Mhz (B40) – Optus (Vivid Wireless spectrum)

So apart from B3 on all carriers I could also use B1 for Vodafone or B5 for Vodafone also. So if I visit there a Vodafone prepaid SIM might be best?