One of the joys of living in a 3 dimensional world (Eat your heart out The Simpsons!) is that there's more than just the East or West - there's actually numerous routes you can take from the US to Australia - including both North and South!
How much these routes actually add obviously depending on where you're starting from - if you're in San Diego it's obviously going to be a different answer than from New York.
For simplicity, let's presume you're starting out in New York. It's not YYZ, but it gives the best options :)
This Great Circle map gives a number of the "single stop" options and their distances.
The most obvious routes are those via the West Coast - NYC-LAX/SFO-SYD (flown by numerous airlines) and NYC-DFW-SYD (flown by AA/Qantas) both come in around the 10,000 mile mark. (The DFW flight has a stop in Brisbane on the way to Australia but not on the way from Australia, and it's basically just a fuel stop and you continue on the same plane to Sydney). Even going via Hawaii is around the same distance, but has the disadvantage that half of the trip will be on a domestic-configured plane.
The next best option is to head North! Going via Japan means going via the polar route, and only adds about 15% distance to the flight - and still only a single stop. Hong Kong and Singapore also take a similar route, but bump the distance by about 25% and 35% respectively. (NYC-SIN is also available only in Business Class - there's no direct economy class flights)
If North isn't your thing, you can always head South! Via Buenos Aires adds about 25% to the distance, although the direct flights EZE-SYD are frequently seasonal so aren't always available.
Finally there's East. There's countless routes heading East, but the majority of them will require 2 stops. Options such as Dubai or Doha, Qatar drop this to one stop, but it's still >40% longer than heading West. Adding an extra stop such as NYC-FRA-SIN-SYD actually makes the trip shorter from a distance perspective (only about 40% over the westerly routes) - but obviously with the disadvantage of another stop.
All up, if you've got time to spare then heading east and planning a stopover somewhere in Europe/Asia can be a good option, but it's definitely going to increase the distance you're flying, the time it takes, and probably the cost. Personally I love the westbound flights - they depart the US west coast late at night, and arrive in Australia about 14 hours later when it's early morning. As long as you can sleep at least a little on the flight, you normally arrive relatively well relaxed and ready to face the day! I've done US-AU 3 to 5 times every year for the past 5 years (from the US west coast, east coast, and central) so I've got a little experience here :)