Australian soldiers are renowned for their bravery under fire in conflicts from the Boer war, WWI and WWII, Korea, Vietnam and peacekeeping missions since then. They are valued more than the typical US soldier as, apart from some in Vietnam, every Australian soldier is a volunteer, who undergoes significant training and development before the battlefield. In Vietnam, whole battalions were replaced, unlike the US system of individual replacements. This allowed the Australian troops to have a higher cohesion and combat ability as there were no 'new meat' to worry about.
The belief about being undisciplined is a fallacy. As a free and equal society it is encouraged for the soldiers to speak up and provide an alternative plan if they feel uncomfortable. This is very similar to the way special forces are trained. Australian soldiers have been acknowledged for their industriousness, ingenuity and natural cunning. During WWI and WWII there were a lot of sldiers from the rural areas who were excellent horsemen and sharpshooters. This has increased the legend. There has also been a lot less drug taking in the Australian Army.
The US soldier and the Australian digger are both well trained and motivated soldiers, but the US Army relies very heavily upon munitions and technology to overcome the enemy, whereas the Australian army is taught superior tactics as the Australian goverment is too stingy with cash for either firepower or high tech. This is slowly changing with the acquisition of M1 Abrams Tanks, Joint strike fighters and the most lethal diesel submarines in the world which have surprised many US seamen on operations.