In terms of number of miles to redeem - United wins hands down.
United also wins in terms of legroom.

In terms of ease of reaching most Australian cities (ie not Sydney or Melbourne) then Qantas wins hands down - to get to other capitals on a United ticket you would need to travel via NZ on Air New Zealand and if you are going anywhere else (including Canberra the national capital) then you'll be on at least one Qantas leg.

Qantas has inflight personal entertainment in economy but less legroom (far less in fact so can be uncomfortable unless you are actually short).

Of course you can redeem Continental and US Airways miles for Qantas flights so for most potential seats US Airways might be better (although any flight will cost more miles).

Delta & Northwest are not real options since it costs 100,000 miles for an economy ticket WAS-SYD and you will have to fly Korean Air via Korea....

Lastly - there are far more Qantas flights per day between the US and Australia the any of the others (and Qantas has something like 80% market share) so more seats (for purchase) and more flexibility in flights (plus the convenience of direct flights from California to Brisbane and Melbourne as well as Sydney)

Of course if you join the Qantas Club you get good benefits with American and BA (in club lounges anyway) and can experience Qantas Clubs which are really nice.......