I think I've discovered the reasons Iran is so focused on its uranium enrichment program.   It's too worried about getting shown up by Canada and Australia.  In 2009, Iran spent $6.5bn on defense.  Canada and Australia, who together have less than three-quarters Iran's population, each spent almost triple -- Canada outlaid $19.2bn and Australia $19bn.   This reminds me of a question I once drunkenly posed in a Laotian bar in 2005.  Which of the two countries, Canada or Australia, would win in a war against the other?  Never mind Iran for now.  The United Nations can worry about that one.

On the face, it's an absurd question.   Both countries are constitutional monarchies with Britain's Queen Elizabeth II as the head of state.  The two nations have deep historical ties and have fought side-by-side when the sun never set on the British Empire and, more recently, in the Korean War, the Gulf War, and the war in Afghanistan.   There's no reason Canada and Australia would ever really get into a fight.    This question is a hypothetical one and asked as much as an exercise in critical thinking as because no immediately obvious answer comes to mind.

A distance of around 7,500 miles (12,000 km) separates Canada's western coast from Australia's eastern one.   That's a fair distance.   As ridiculous a notion as it is that Canada and Australia would wage war on each other, it's even more ridiculous to imagine one transporting troops and materiel to the other for the purposes of war.  The two would have endless arguments beforehand deciding who gets to host the fight.  To lead this thought experiment along a fruitful path of discovery, it's necessary to set up a few ground rules first.

  Since both Canada and Australia possess primarily defensive forces, each would be at an advantage if the other tried to invade its lands.  The war has to take place in a third country or territory more or less equidistant between the two nations.  One possibility is the Pitcairn Islands, located 5,133 miles (8,260 km) from Vancouver and 4,664 miles (7,506) from Sydney.    Less than 50 people live there, and there's only one settlement on the island. 

      Both countries have three weeks preparation time to get their forces amassed on the island.  We will assume that neither nation will launch an assault on the other within this three week period.  Without that assumption, the nation that set up shop first on and around the island in greater numbers could fight in defensive mode and probably prevent the other nation's forces from ever landing.   The point of discussion here is to avoid one nation being mainly defensive and the other offensive. 

  Each nation is completely on its own.  Neither gets any logistical support, weapons, materials, or military assistance of any kind from other powers.  The forces and weapons available to each nation are those it possesses in its arsenals as of the end of 2009.

Strength of a nation's military depends on several factors:  proper training, adequate investment, size of fighting forces, technology, and experience, to name a few.     We'll take for granted that both countries' forces are equally well trained, that a Canadian fighter jet pilot, sailor, and infantryman are equivalent in raw skills, on average, to their Australian counterparts.   Canada has its Joint Task Force II.  Australia has its Special Forces.  Both are elite units and which is the better is all a matter of opinion. 

Canada and Australia each have the same military budget (denominated in 2009 U.S. dollars), but because Australia's economy and population is smaller than Canada's, its share of military expenditure is a greater percentage of its GDP -- 1.8% for Australia vs. 1.3% for Canada.  The absolute dollar figure is the more important one.  A submarine, air force jet, and missile all have the same market price whatever the size of the country's GDP.  Naturally, a country with a bigger economy can reap greater economies of scale buying or manufacturing military equipment.  The percentage of GDP figure is more a gauge how serious a country takes its military.  Israel, for example, 'only' allots $14.3bn annually to its military budget, less than Canada and Australia, but this is 7% of its GDP.   Canada's and Australia's percentage figures are on par with Sweden, Norway, Denmark, and Holland.

Fighting force size counts up to a point.  In the Winter War of 1939 between Finland and the Soviet Union, the Soviets had three times as many soldiers as the Finns.  The Finns fought better, but the Soviets could sustain the greater losses.  The Canadians have 67,756 active personnel and 23,599 paid reserves.    Australia has 55,068 active personnel and 25,493 reserves.    Those are not formidable numbers on either side.  As a comparison, there were 112,000 American troops in Iraq as of December 2009, an amount equivalent to the sum total of all actives in Canada and Australia.   Bear in mind that neither nation would be in a position to send all of its active troops. 

In today's wars, technology matters more than absolute troop numbers.  Canada's potential 23% advantage over Australia in soldier count may be no advantage at all if their military equipment is inferior.   Canada has a total of 391 aircraft in its fleet.  Its primary fighter aircraft is the McDonnell Douglas manufactured CF-18 Hornet.  The Canadians procured 138 of them between 1982 and 1988, and 80 were still operational as of 2008.  In 2000, the Canadian government modernized the aircraft.   The shelf life on the upgraded planes ends between 2017 and 2020.   

Australia has a total of 270 aircraft.  It uses an almost identical fighter plane, built under license in Australia, called the F/A-18 Hornet .  71 remain in use, putting it almost on par with Canada.  The Australian planes are in worse shape and plan to be retired in 2015. 

In an all-out air battle, the Canadians' numerical superiority in soldiers and slightly newer planes could prove a deciding advantage.  However, with the war taking place more than 7,000 km away from either country and neither in possession of an aircraft carrier to transport the aircraft the vast distances to the fight zone, each would only be able to send a handful to the war theater.   Thus, neither side is likely to have an evident air advantage. 

The respective navies and armies would play a more important role.  The Canadian Navy operates 33 warships and submarines.    Its backbone is 12 frigates which entered service in the early and mid 1990's.  They are capable of carrying helicopters, anti-submarine torpedoes, and anti-aircraft and anti-ship missiles. The frigates are supported by 3 destroyers built in the early 1970's, 12 modern patrol boats, and 4 submarines.  

The Royal Australian Navy more than matches this with 54 commissioned vessels.  They have 8 anti-submarine and anti-aircraft frigates capable of carrying a Seahawk helicopter plus 4 more frigates built in the mid 1980's -- 12 in total, like Canada.    There are 14 modern patrol boats and 6 submarines.  Considering that Australia is a large island nation with foreign attacks feasible on its western, northern, and eastern coasts, whereas Canada has just two penetrable coastlines spanning a fraction of the distance, a top notch navy would be more essential to national defense Down Under than it would be in Canada.   If the two navies engaged in battle, Australia would be better prepared to win. 

The Canadian Army consists of three field-ready brigade groups.  Canada produces its own infantry fighting vehicle and anti-tank guided missile.  Even with severe cuts in the Canadian military budget, the Army hasn't suffered.  They operate 10,500 utility vehicles and 2,700 armored fighting vehicles.  

The Australian Army also has three brigades, but it is mainly a light infantry force geared towards low-and medium-intensity operations.   The Australians' key military operations in the past have been in Asia where light infantry forces were effective.  In concert with its allies in bigger operations, Australia is known for high quality niche fighting forces.

If the two armies were meeting on a battlefield in Europe in ratios equivalent to the total active forces in each nation, the Australian Army would get a thrashing by the Canadians' mechanized equipment.  But because they're meeting on a South Pacific island midway between them both, an island we can surmise is dense with jungle, the Australian Army's expertise in jungle warfare, patrolling, and ambushing would give it an edge over the Canadians. 

The number of army personnel available for fighting on the ground is determined by how many troops each country can get on the island in the three week preparation period.  With no assistance from other nations forthcoming, Canada and Australia would have to get most of their troops to the war zone by sea vessels -- that is, rely on their navies.  We'll assume the airport/landing strip in the Pitcairns will not permit the landing of commercial airliners carrying military personnel.  At the end of World War II, Canada possessed the third-largest navy in the world.  Today, Australia has the larger navy of the two (though not by much) and a technologically sophisticated one at that.   A larger navy means transportation of a higher percentage of troops.  Let's say that each nation has 20% of its national fighting force it can spare.  Canada would have a maximum of 13,500 it could send, and Australia 11,000.  We argue that Australia's more wavewise navy would be able to get a greater percentage of available troops to the war theater than Canada's.  In turn, despite Canada's greater pool of soldier talent, each side has about the same number of soldiers in place when the fighting actually begins. 

The weak spot with both nations' military forces is independent combat experience.  Canada has little experience in offensive military tactics on its own.  Defense cuts in the 1990's severely undermined its forces' fighting ability.   Canada's armed forces are designed for, first, the defense of Canada; then, the defense of North America in conjunction with the United States.   The Canadians know that no threatening enemy power could get within a time zone of a Canadian coastline without the U.S. military stepping in.  Therefore, Canada's real defense role becomes one of working along with the U.S. to provide marginal assistance in North America's defense.   

Australia originally relied on its British and American allies to provide its key defense.  In 1969, the Nixon Doctrine put forward by the United States stated that U.S. allies were now expected to take care of their own defense, though the U.S. would provide assistance if requested.  Australia initiated its Defense of Australia Policy.  Military forces were concentrated in Australia's north facing the Asian continent to prevent an attack.   Over time, Australia gradually increased its ability to strike at enemy forces abroad from its own bases in Australia.   These changes have not transformed Australia into a military powerhouse.   Not in the least.  Australia's logistical capabilities remain insufficient to supply their military forces deployed far from home.   In the past, Australia was always part of a team of larger coalition partners -- usually, the British and the Americans -- who provided that logistical support. 

Canadian forces have no recent experience being deployed abroad as the sole or leading power.  For that matter, they lack a lot of recent fighting experience period.  Long thought of as a nation of UN peacekeepers, ever since the 1990's Canada's contribution to UN peacekeeping missions has been in steep decline.  As of 2006, Canada ranked 55^th out of 108 troop contributing countries.  In 2010, Canada rejected a UN request to lead a Congo mission.  Put more accurately, a Canadian general turned down the chance to lead a 20,000+ peacekeeping force, only of which a few dozen would've been Canadian.  Canada's biggest recent fighting commitment, but done so in partnership with its powerful allies, is in Afghanistan, where they have approximately 2,800 troops. 

In contrast, Australian forces conducted a military operation, Operation Morris Dance, in reaction to a Fijian coup in May 1987; and in 1999, led the peacekeeping effort in newly formed East Timor.  Australia is also in Afghanistan, contributing 1,550 troops.  Australia doesn't have volumes of experience handling or disproportionately contributing to major offensives, but it has some front line experience and some is better than none. 

It's this real world fighting experience that contributes the most to a victory.  Great technology is necessary, but if the forces using that technology have never had genuine uses to employ that technology in the field on their own, the technology cannot be utilized to maximum effect.   Let's look at Saudi Arabia.  They spend 8.2% of their GDP on defense.  That's $39.3bn, slightly more than Australia's and Canada's military expenditures combined.  With this cash, they buy the most modern military technology from the West.  And yet if Saudi Arabia were to be invaded or the mere threat of an invasion appear on its doorstep, like it did in 1990 when Iraq invaded Kuwait, the Saudis know they can count on the United States to back them.   If the United States refused to help and the Saudis were left with their high-flying technology to fight solo, would they win, especially against a nation which had ample recent fighting experience?    

Canada and Australia are not military juggernauts.  A war between them is like two paunchy and out-of-shape arthritic 65-year olds getting into a scuffle.  No side really wins.  One side just collapses before the other.  Neither tips the scales on all significant military measures. Canada has more troops,  Australia spends more per capita on defense.    Canada's Air Force is slightly more equipped than Australia's, but then Australia's navy is slightly better outfitted than Canada's.  The Canadian army has more equipment than the Australian army, but all of this equipment would prove ineffective in a jungle island war environment.    

The deciding factor in a military victory between the two scrawny forces remains the experience.  Both nations rely heavily on U.S. security guarantees to keep their derrieres safe.  Canada, having big brother right next door, is less self sufficient than Australia thousands of kilometers away.  Australia has the largest military in Oceania.  That ain't saying much when Oceania consists of Australia, New Zealand, and many tiny South Pacific islands.  But at least Australia is a big fish somewhere.  It's evolved into a very, very, very lightweight regional power, which means it has to step up and show some meager independent fighting initiatives in its own backyard.   Canada's geographic situation prevents it from having to do even this. 

Verdict:  Australia's ranking over Canada is not restricted to Australia's better-tasting Cadbury chocolates.  In an all-out war, the kangaroo would hop all over the mountie.