Koala:
Something interesting happened to me this Xmas. I wa seeking to get a Award ticket to fly SYD or MEL -> AKL ! Well,... my main FFlyer program is with VARIG so I went straight to UA to try to book a ticket (Star alliance thought ....). No way ,... couldn't get it months ahead. The second option was Thai (Star again ...). No way !
So ,... I got it with AirNZ on the first try ! Detail : to travel on the 21/DEC on a very busy 737 service across the Tasman !
My conclusion was that UA would never give the award ticket to me on this route just because I could be taking a place of someone PAYING SYD->USA !
If you stick to the local airlines ,... for sure you have a better chance. Doesn't matter if it is star, oneworld or whatever !