You get used to long haul fairly quickly. When I was working full time I often did Brisbane -LA-Vancouver, and once a year it was onto Toronto after a couple of days in Vancouver. What I did not enjoy was arriving in LA at 6am then waiting until around midday for the Vancouver connection. I like either just a couple of hours stopover, or overnight.
Going to Europe was longer, and typically would be a short stopover in Singapore and then change to the plane that had come from Sydney or Melbourne. Onto Europe was overnight, so sleep for a lot of the hours. But I did prefer to do the single stop in Dubai. I long flight to get there, a shower, clean socks and underwear during the 2-3 hour stop and back on board for the final hop. Although that was 6-7 hours you felt as if you were almost there once in Dubai!
I had a few trips to the Azores from Brisbane. The Azores are almost at the antipode of Brisbane, so in theory you could go either west or east and it would take the same time. Normally I went west, to London, then to Lisbon where it was overnight before out to Horta the following morning. It was OK. I nice walk and some drinks and light meal at Peter's Cafe Sport overlooking the marina perked me up pretty quick.
But on one trip I went East. That was Brisbane - LA - Boston, with a quick connection in LA. Then it was overnight from Boston to Ponta Delgada which was good also. But the killer was about a 6 hour wait there for the commuter connection to Horta via Terceira. I don't remember elapsed time from home to Hotel but it would have been more than 36 hours. I only did that route once!
So, Sydney to New York non-stop? Probably OK. It all depends on who else is around you, which you have almost no control over. Someone snoring, or having the reading light on when most people want to sleep is a bit annoying. I always take an isle seat so I can move if and when I want. But how often the person next to the window wants to get past you, and when, also impacts your own sleep pattern.
I do like travel from the point of view of the places I visit, but flying to get there - no fun any more. Including the whole departure and arrival process and transport to and from the airport, I regard flying as a necessary evil to be minimised these days.