I believe the number of ISPs differs regionally (I suspect due to where they have network equipment), but I just put in my adress into the main search website (https://www.broadbandcompare.co.nz) and it came back with 13+ ISPs (although some of them might belong to same parent companies). Prices tend to be quite similar (which I suspect indicates that it is operating close to cost) and differentiation happens mainly on bundling with other services (mobile, power, TV, included Netflix...) Keep in mind that I have only lived here for 1.5 years, but from my limited experience it definitely seems like there is a healthy amount of competition.
Chorus does let ISPs handover in just a single or a couple of points to provide service nationwide (well, for the areas they serve), instead of needing to do it at all 27 handover locations. I imagine it's possible to interconnect with the other fibre companies over a backhaul connection as well. So smaller ISPs can definitely offer service nationwide without having to put networking equipment all over the country.
My understanding is that the margins on fibre connections for ISPs are quite slim. The three big telcos do both broadband and cellular, and they definitely try and push customers with lighter needs over to wireless internet delivered over 4G or 5G (which has more margins for them). There has been a bit of consolidation among the major players (one of the big telcos (2Degrees, who do both broadband and cellular) merged with one of the big broadband-only telcos (Vocus) a couple of years ago). But there's plenty of smaller ISPs. And a couple of the electricity retailers have gotten in on providing internet as well. And it's not uncommon for local WISPs to offer fibre as well.
Differentiation between ISPs is definitely mainly on cost, quality of support, and bundled services. They all have their own networks (the fibre companies only provide L2 connectivity from the customers to the ISPs), and there can be some differences there. For example, another of the big broadband+cellular telcos (Spark, who was the ISP side of Telecom before they were split up) is the only major ISP that doesn't offer IPv6 and doesn't peer at local peering exchanges.
Some ISPs have cheaper plans with data caps, but many ISPs don't even offer data-capped plans, and everyone offers uncapped plans. Similarly, most ISPs let you use your own router. And about the only variation in how you'd need to configure your router is PPPoE vs IPoE/DHCP and VLAN 10 vs untagged. So you can usually switch ISPs and all you need to do is maybe change your router config.
As a side note, of particular interest to the audience here is the existence of a new-ish residential ISP (Quic) that offers things like static IP for a one-off cost, /28 IPv4 subnets, self-service rDNS management, and self-service access to the ONT status, connection logs, etc. One of the advantages of having competition in the ISP space.
