In my opinion if your itinerary is a valid Oneworld Explorer AND a valid Global Explorer, then there is no reason to favour one over the other.
(I am part way through my first ever Global Explorer - chosen because I am visiting six continents for the price of four
)
the major differences between the Oneworld and Global Explorers are:
Base Fares:
Oneworld - base fare depends on how many continents are in the itinerary
Global - base fare depends on the mileage (and for premium cabin there is only one allowed mileage - 34,000)
Generally the DGLOB34 has the same base fare as the DONE4 (they are slightly different ex-Norway)
Stopovers/Flight Segments:
Oneworld limits the number of flight segments in a continent (max of 4, except for Nth America where 6 is allowed)
Global limits the number of stopovers per continent (max of 4 for each continent)
Trans-continental flights:
Oneworld has limits on trans-continental flights (in Nth Am and Australia)
Global does not
Your itinerary is a valid Global, but an invalid Oneworld - it has two trans-cons in Nth America where only one is allowed (you have JFK-PHX and BOS-LAX)
Additionally, are you aware that Qantas flies JFK-SYD direct? (It is via AKL)