The post-war assessments are going to be interesting. Every side is going to have something to learn. Britain will, for her part, feel smug in her naval superiority, but her army will have for the third time in less than a decade been almost emptied from the Home Islands and the Colonies in order to respond to a major war, while needed to raise many new regiments. It's not exactly a sustainable or economic model overall!
The United States will have learned that a great big army means nothing if you can't supply it! The hammering they've taken from modern rifles and artillery is also going to cause some serious reconsideration of army doctrine and training. Their semi-complacency around naval matters (and TBH relative inexperience) is going to show. The question will be whether they need a battlefleet like the European naval powers, or should they invest in more ocean going ironclads which can show their strength both abroad and at home. There will be a lot of debate post-war in naval matters, but this was an era of transition for the world's navies so there's plenty of room for debate...
Canada has learned that Britain will indeed defend them, but whether that kind of dependency is a good or bad thing remains to be seen...
Third time? Crimea and ?
It still blows my mind that iOTL that the US Military dropped so much in size between the end of the US Civil War to the 1890s. Unless things get *really* sunny between the US and UK/Canada, I just can't see it dropping as much.