Definitely ban any and all forms of deep-sea mining in New Zealand, at present. There is no legislative requirement (a loophole in NZ legislation) for them to undertake any environmental impact assessment/appraisal prior to commencing their operations. Until the legislation catches up with activities (tourism, mining, fishing, spoil disposal, aquaculture ...) that affect the sea bed/water column outside an effectively, arbitrarily chosen 12 nautical mile distance from mainland NZ and offshore Islands, then no permit should be issued to anyone to do this sort of thing. In years to come we'll be ashamed of what we allow to occur today.
The area that Neptune is most interested in is around hydrothermal vents. They maintain that the impact will be localised. That's no comfort to the animals that are also localised and 100% dependant on the vent itself - the area of greatest interest to these prospectors. Localised impact/effect means complete annihilation of a unique community.
So, outright, indefinite ban on any such activity until we know something about the communities that occur there, the distribution of those communities over greater spatial scales, and we reach some management/conservation plan to ensure that adequate, sustainable and representative communities remain. Should China need copper then let China mine its own waters; should the French wish to test nuclear bombs let them test them on their own mainland; should a country wish to dispose of nuclear waste then let them do it in their own waters; should the Japanese wish to eat whale meat then let them slaughter whales in Japanese waters!