For service (and price), Emirates take some beating, but the seats are not the best in class.
For better seating, then either BA or Qantas are probably the best - I think that all Qantas flights UK to Sydney are now flat. I personally don't notice the difference between the "angled" flat and the BA arrangement - as long as the seat goes flat, it works for me.
QF service is better than BA in my experience as is the wine. Sydney to NZ would be on a 767 with older style seats, but it's a short flight compared to getting to Sydney.
Time wise, I don't think it really matters - it's a long trip.
I would also avoid going though the US at all costs. The hastle now is just not worth it.
I always used ebookers in the UK to get the best prices on flights. Pity they don't operate down here.