The advantage with Canada's independence is that we got it by asking nicely and without anyone having to die
Lots and lots of Canadians died prior to the Imperial Conference of 1930 (and the subsequent Statute of Westminster, 1931), with hundreds dead in actions specifically to free Canada from control by the British Cabinet. It is precisely on the basis of those deaths that Mackenzie-King (cf. Mackenzie, several paragraphs below) was able to lead the Conference to the principle that all the Dominions should have both legislative and foreign policy independence and control of their own militaries.
After 1931, even the formal ties were effectively cut: the Judicial Committee of the Privy Council had a subcommittee of Canadian judges who had *exclusive* appellate jurisdiction; the British government agreed that they would pass without amendment any Constitutional legislation Canada required provided the federal and provincial governments were in agreement (of which there was a strong lack readily visible to all onlookers until no earlier than 1982, and even then at least one Province claims to have withheld critical agreement on the formalization of the amending formula and the entrenchment of specific Acts).
1931 also marked the final time when Canadian troops would be summoned by the Imperial government to fight in wars directed by the Cabinet in London.
Compare with the various post-Boer War mutinies by Canadian troops condoned by the Canadian government. An example: when conscripted Canadian troops were held in awful conditions in Wales due to British government vs Canadian government conflict in de-deployment and repatriation policy (the British government were fairly plainly trying to keep the Canadians in service, in part because they cheaper and less politically connected than English troops):
"In all, between November 1918 and June 1919, there were thirteen instances or disturbances involving Canadian troops
This sort of thing led to a lack of conscription in Canada during the first part of WW II, and later on a plebiscite/referendum on the question of conscription late in the war (in April 1942) led through a series of compromises to the result that few conscripts actually left Canada and fewer still ended up on the front lines of the war (less than three thousand) -- the Canadian conscripts were mostly deployed to free up volunteers (and British conscripts...) from non-combat posts. It is entirely possible that had the Canadian government caved in to British demands for troop numbers and introduced conscription early in the war, Canada would have exited WW II before Pearl Harbor. Indeed, it is mainly Pearl Harbor and the entry into the war of the United States that led to the passage of the referendum at all.
Earlier in Canadian history there were even small-scale uprisings -- one might even call them revolutionary or civil wars -- that led to deaths and reprisals. Among them were the rebellions of 1837-1838 (William Lyon Mackenzie, Mackenzie-King's grandfather, declared a Republic of Canada and led armed skirmishes in what's now southern Ontario; Papineau, Storrow Brown, Chenier, Oklowski and the Nelsons led armed uprisings in and around Quebec City and Montreal -- a couple hundred dead all together, thousands wounded, and scores of executions and deportations to Australia). There were occasional low-level disturbances of the peace in Ontario, Quebec, New Brunswick and Nova Scotia more or less until the end of the U.S. Civil War at which point the anti-Republican parties that controlled the governments that confederated to form Canada and the British government agreed that self rule and full representation-by-population and universal adult male suffrage (neither of which Britain yet had in spite of the (Great) Reform Act of 1832) was the only way out of an eventual second North American Colonial Revolution with Britain and the United Empire Loyalists, and more specifically the supporters of the British Tories, again on the losing side.