Travelling SYD-LAX-JFK isn't so bad as the flight times are (although marginally) shorter. You have an early arrival into LAX and by the time you get to JFK the day is done.
JFK-LAX-SYD though is not a pleasant experience. The JFK-LAX sector can be 6 hours flying plus all the potential ground time at Kennedy. The LAX-SYD is a killer then which arrives in the morning. I've done JFK-LAX-BNE-SYD in J, slept half of JFK-LAX and most of LAX-BNE and even then I felt like death on arrival.
So... If you want to break it, I'd suggest doing it on the return. As mentioned, JFK-LAX is **** - doesn't matter if you take AA, UA, DL or whoever, they all rival Jetstar.