A few points:
- A 777 is more fuel-efficient then a 747 for a few reasons, including engine design, wing design, and airframe design.
- The 777 was certified for ETOPS 180 when it entered service, so UA is allowed to fly up to three hours away from land heading down to SYD. Essentially, the 772 and 774 fly the same routing.*
- The cruise speed of a 744 is Mach 0.85.
- The cruise speed of a 772 is Mach 0.84.
* - The Great Circle Mapper site at
http://gc.kls2.com/ will show you the various tracks using ETOPS 60 to 330 mins.