It is quite possible that the ANZAC replacement will be a low end frigate designed to increase fleet numbers in the Australian Navy. With the introduction of the Air Warfare Destroyers we no longer need frigates with all the bells and whistles.
So we may end up with a basic frigate with high levels of automation with only light anti-ship and anti-air capabilities. Such a vessel will be within budget of New Zealand.
Though to be honest they should just reduce the manning on the ANZACs and keep using them but in a low end role. As technology progresses around us, if we stop upgrading them they'll move from a modern high end frigate to become a low end frigate. Put in some off the shelf computer to improve automation during a refurb and keep sailing them.
So then New Zealand has an old ANZAC frigate that can perform handle itself well. The Australian Navy has a low end frigate that is cheap because they didn't have to buy new ships. The High end is then made up of Air warfare destroyer.
Not to be offensive, but the Anzac frigate is a relatively low-end frigate. It is only on the more recent RAN built Anzacs that were built with ESSM in place of RIM-7, and those vessels that have been backfitted with Harpoon capabilities that are becoming formidable. Compared to the older RAN Adelaide (mod OHP/FFG-7) frigates, they are inferior warfighting ships in basically all areas except for main gun AFAIK. Sonar could be a different story though.
All around both the RAN and RNZN Anzacs were constructed with fairly basic armament, being "fitted for, but not with". It is only as some of the RAN vessels are approaching their mid-life update and the Adelaide-
class is being gradually decommissioned that additional systems are being fitted to expand the RAN Anzacs' capabilities.
If the RNZN wanted to keep a low-end frigate in service, then likely the best thing for them to do would be to just update the physical plant/machinery of their Anzacs to keep them in service.
As for any future RNZN Anzac replacement, I would tend to think the best path to follow would be joint participation with the RAN Anzac replacement. Failing that, then a MOTS purchase of some NATO/allied power general purpose frigate.
For overall numbers, three capable frigate would seem best, but if the choice were between two capable frigates or three less capable frigates (fitted for, but not with again...) I would likely choose the greater number of less capable ships. Of course, much depends on what is occuring on the world stage, if there is a great deal of tension, with a high likelihood of hostilities breaking out before an upgrade program could be initiated, then having more capable ships would likely be a better choice.
As stated by others, a concern would be a decision by the NZ government to replace the frigates with corvettes, or worse yet, OPVs. A corvette being basically a cutdown frigate (or heavily armed OPV) with insufficient range & seakeeping to patrol away from NZ. An OPV would IMV be even worse, despite a prediction of being able to fufill ~80% of the frigates current role. I have to wonder how much of that is occurring because the frigates have been getting assigned to EEZ patrol duties because NZ does not have anything else to use at present.
Even with some of the upgunning of OPVs mentioned previously, an OPV could not adequately act as a ship escort, ASW asset or interdict hostile shipping. All roles that the frigate is able to do (some more so than others given current fitout). What hopefully will occur is that more people in NZ will become involved, and take a serious and realistic look at what they are asking the NZDF to do, what the NZDF can do, and what it likely needs to do.
-Cheers