It's totally subjective, but some factors that might influence your decision are whether you are travelling on an award ticket or paying, and whether you are flying Y, C, or F. It really depends on what type of flier you are. Perhaps you could post some more details on exactly what you need recommendations on.

You have two nonstop options from the US Mainland - either QF or UA, from LAX or SFO. Personally, I'd fly US to LA or SFO, and QF to SYD. QF's service, comfort, and IFE are better than UA's. You can also, for now, earn US miles on QF. I know that partnership is coming to an end, but don't know the date...it's definitely this year, but I'm not sure if it will be over before your trip. Still, if the partnership is over, you could book the QF ticket and credit the miles to AA.

As far as UA - service is good, the 744s are a little worn; but if you are flying in Y and can score an E+ seat, it's a good choice.