I believe the ties between Britain and Australia are weakening by the moment. Australia sees itself as multi-cultural and Asia/Pacific oriented, not British any more. America is its preferred partner now, in politics and economically. Canada, with its common border with the US cannot help but be influenced more by America than by Britain, even if it hasn't made the positive political choice that Australia made, to strengthen ties with America at the expense of ties with the Motherland.
In WW2, Australia fired the first shots of the war against a German ship, within hours of war being declared in London. Canada chose to wait a week before joining in, to emphasise its freedom from Westminster. Both countries are now taking part in the Afghanistan War, not (to my way of thinking) because Britain is there, but because they have their own relationships with America to foster, and they would have joined in even if Britain hadn't.
There are still Aussies who see themselves as Australian-Britons, and there are still many Canadians who think the same way - a few still add the letters UEL after their name, but I fear the links are weakening as both countries begin to assert their identities in the world. Canada seems to be going about this much more quietly than Australia (whose politicians (not people) seem to display resentment and scorn against Britain (the people just see Brits as a joke!)). I think it will be Canada that turns out to be the more influential of the two.