UA could do a status match (search on that in Miles Buzz forum). Great awards (especially within and from NZ/oz), however earning rate is not too good unless you fly UA (once have status).

NZ has great earning rates in first and business (200+% equivalent in airpoints dollars currency) but is a bit expensive on the award side and heavily skewed to those who fly NZ (eg annual fee if no NZ flights).

SQ has lower earn rates (only 1.25 for business, plus status bonus 0.25 when flying SQ). However if you plan on flying SQ business/first a bit then definitely sign up for Kris Flyer regardless of where you decide to credit miles/go for status - this is to attain PPS status which can be double dipped. See SQ forum for lots more info. From AKL one round trip to europe on SQ in business is more than half way to (re)qualifying for PPS.

BD and LH both have good earning rates in business/first (200% business, 300% first, 150% full economy). LH has a higher requirement for *G (at 100k) but this includes any status bonus (25% on certain airlines) and requalifying is only needed every 2nd calendar year. BD has cheaper awards than LH but status bonus doesnt count towards requalifying and need to requalify every year.

Edited to add - there is a wealth of information linked through the sticky *A useful reference links, especially BlondeBomber's *G comparison table.