Flown this route many times. Here's my judgment:

UA: Worst, but improving

NZ: Best, but getting worse

QF: In the middle

As others have pointed out, the terrible UA 744 is leaving this route and by May will be a 772. You'll still get bad food, non-free drinks and indifferent service, but you'll get passable IFE (still the worst of the bunch) and a reasonable seat, plus it's nonstop saving you quite a few hours. If you can get E+ I'd actually say it's the best option now.

NZ is tricky because it depends what metal you're on. Avoid the 773 at all costs -- it's shiny and new but has ten-abreast seating in economy. The 772 is old and has a worse IFE system (still better than UA's) but is only nine-abreast. The 744 is really old and tired but theoretically has a bit more legroom so could be the best option. On the SFO-AKL route you'll get a 772 or a 744 for now, but it will be changing to 773 later in the year. NZ will give you the best food, booze and probably service. AKL is a far better place to change planes than LAX, but not nearly as good as not changing planes at all.

QF will give you a shiny new A380 with a surprisingly wide but otherwise-lacking seat. Excellent IFE system, food slightly worse than NZ but much better than UA.

What would I do in your situation? I think I'd be tempted to chance it and go with UA in the hopes of getting E+. (Or just pay the extra for E+). On a 13-hour flight I care about seat first, IFE second and food third.