SYD-SCL is the same aircraft as AKL-SCL but sometimes there might be availability on SYD-SCL and not on AKL-SCL (and sometimes the other way around). Similarly due to the way QF's codeshare works there may be availability on the QF code and not on LA's or vice versa.

The only other direct(ish) flight options to South America are Air Tahiti Nui (as far as PPT then take LA) or Aerolineas Argentinas.