Asking what is the difference between UA and SQ is like asking what is the difference between a Ritz Carlton and a Motel 6.

While UA does have E+, the pitch and space on the 747 that flies the Australian route is among one of the worst. Without this edge, UA basically has no advantage over SQ, period. Since this is an award ticket, bonus miles and other perks don't matter, so you should definitely get yourself on one of the better airliners like SQ.

NZ is also one of the better airliners, but I would still go with SQ, definitely one of the best (if not THE best) airliners in the world.