For economy travel on this trip, and not a frequent flyer on *A, I would not join Air NZ. NZ Airpoints is revenue based and geared towards those who regularly fly on Air NZ.

If you don't have much other *A flying then status is not likely a major consideration for you. While you might get a low level status on either BD or SQ programs purely from this trip (I haven't checked the maths), the benefits are not much. BD silver lounge access when flying BD is probably the best benefit of a meagre lot.

So, for me the main factor is how many miles will you collect and will it be enough to redeem for an award which you'd like to take. BD is probably better for you than SQ, but it depends on where you want to travel on the award.