February is our peak month so have you booked the campervan yet? What parts of NZ do you really want to see? I don't think either way is 'better' but you might find the decision made for you with the campervan rental availability or the flights back to Auckland or however it works out.
Auckland starting point:
Waitomo / Hobbiton / Rotorua / Taupo
then either drive through the centre of the North Island OR
Napier / Hastings / Hawke's Bay / Wairarapa.
You need to end up in Wellington to catch the ferry across Cook Strait.
Then Picton / Hanmer Springs /Kaikoura / Christchurch.The earthquake damaged road may be fixed by then but it may not. So driving the coast road to Kaikoura may not be an option.
OR Picton / Nelson / Greymouth / Fox and Franz glaciers / Wanaka / Queenstown/ Mt Cook / Christchurch.
From Picton
Christchurch starting point :
Lake Tekapo / Mt Cook / Queenstown / Milford Sound /Wanaka / Fox and Franz / Greymouth / Nelson / Picton.
then the North Island in reverse.
Auckland is bigger for more van rental options but a dropoff fee will be charged.It's a lot of driving and our roads are pretty narrow and windy and it takes longer than you think. But 6 weeks is a great amount of time for a good look at NZ!

oops wish there was edit on Fodors...penultimate sentence is 'it's lots..'

We have just returned from 7 weeks in a campervan, our third such trip. We have always gone from Christchurch to Auckland. This has been for a variety of reasons:
1. The weather. We have always gone in winter/spring and enjoyed starting with the cold weather in the south and ending up with the warmer weather in the north.
2. Campervan rentals have always worked out cheaper picking up in Christchurch and dropping off in Auckland as most people seem to do it the other way around and rental companies need to relocate vans to Auckland and some charge an additional drop off fee.
3. Not sure if it will apply to you as we generally fly via Sydney from Europe/Asia but flights always seem cheaper flying into Christchurch and out of Auckland.

Thanks to you both for the great feedback. Yes, so far there's availability with the Escape company. We'll just have to bear raised eyebrows from passersby seeing two old farts driving a psychedelically painted van.
Looks like a $300 savings to start in Christchurch and end in Auckland. Or if we did the pick up and drop off at same location, there would be a 10 percent savings (about $450).
Would it make sense to do a circle route, picking up van in Christchurch, heading south to Milford Sound, driving along the west coast northward, crossing to the NI and encircling the island before turning back to end up in Christchurch?
Again, apologies my ignorance. Once I can decide on flights and van rental, I'll do more thorough research and fill in my itinerary.

"Would it make sense to do a circle route, picking up van in Christchurch, heading south to Milford Sound, driving along the west coast northward, crossing to the NI and encircling the island before turning back to end up in Christchurch?"
Even in 6 weeks that is an awful lot of driving and 2 ferry crossings so I will say no. Try and go one way only and then fly back to your departure airport. If the Kaikoura road is open that is a lovely drive (well it was!) but otherwise you are stuck with that same route back to Christchurch.
If you just went north to Wellington to Taupo and then back to Wellington via Napier/Hastings that might be doable. The North Island is quite wide and up to Cape Reinga is a very long way so depends where you want to go.
Crellston will have an opinion as he has done the campervan thing. And that's a good point that vans are cheaper in Christchurch. If you can do the opposite of the masses then it will work in your favour.
We have a long weekend nationwide on 4-6 Feb which is busy and Chinese New Year is 16 Feb brings hundreds of Chinese visitors here especially to Queenstown so avoid being there then.
If you love swimming then try and get to Kaiteriteri Beach or anywhere in the Abel Tasman National Park for a swim at a golden sand beach and lovely blue/green water.

More like thousands of Chinese...this year's estimate was 33,000.

It is going to cost you around $300 each way on the ferry which would negate the savings you quote, plus, the area around the south of the NI is one of the less intersting areas in the country.

In planning a sensible route, a lot depends a lot depends on whether the road to Kairkours is opened by Feb. This time we missed a lot of the "traditional" as we had seen them before and tried to get to the less visited places. A good place to start is to order a hard copy of this map https://www.newzealand.com/travel/library/p23573_23.pdf

They will send them anywhere in the world. The hard copy is a lot easier to follow! You can do a lot worse than picking out a few of their scenic routes to incorporate into an overall plan.

We have generally headed south down the east cost or inland with a diversion to Mt Cook etc, down south to the Catlins and back up the west coast, cross over to the Golden Bay, Abel Tasman Area, Marlborough Sounds before jumping a ferry in Picton for the North. I would plan on spending more time on the South Island than the north.

I found the https://www.aa.co.nz/travel/time-and-distance-calculator/ invaluable both in initial planning and on the road.

Great point from Tasmangirl re the influx of Chinese tourists. Avoid the major centres at those times in favour of somewhere more remote or quieter. One of te joys of a campervan is the flexibility to use commercial campsites, DOC sites or legit freedom camping sites (assuming you are fully self contained) as well as changing your itinerary at will. Although as you are travelling in high season, you may have to book in some places.

Are the Escape vans self-contained as far as toilet facilities go. If not then you will only be allowed to camp at camping grounds with bathroom facilities. I had a quick look at their website and they don't look to be self-contained.