The "old style" seats are the Dreamtime business class seats. Skybeds are becoming more common the LAX routes, but should be pretty much certain by Feb on the QF8, QF12 and QF108 flights. According to Qantas these three flights will be Skybeds by the end of January. However, some of the other 2-class services such as QF176, QF26 and QF104 will not have reliable skybeds until the end of the year.
So if you are on one of the three flights mentioned above, then I would be asking Qantas why it is not scheduled ofr skybeds. Also note that aircraft substitutions do happen and there is no guarantee that it will not change even the ady before you travel.
I would not look to United since you will have no chance of a flat bed on a United flight. Qantas are the only ones flying the South Pacific with flat beds in J. The only other option for a bed is CX Hong Kong or SIA via Singapore and that add a lot of time and an extra connection to the flight.
See
here for Qantas' roll-out schedule for Skybeds.
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