Any conflict between the two would likely be fought over something in North America/Caribbean or the Pacific/East Asia.
The US became the world's largest economy in the 1890s and was the leading industrial power by that point as well. As such, due to it having massive amounts of raw materials, being geographically closer to wherever the conflict is fought, and having its industries closer to the field of battle (making resupply far more efficient for the United States).
Meanwhile, the UK not only has to fight the industrial machine that is the United States, but it also has to maintain the entire British empire. This is an empire that requires massive numbers of men to maintain and has to use massive parts of its navy to secure its sea lanes and fight pirates, meanwhile the US can afford to focus all of its efforts on fighting the British in its backyard.
The US would win such a war, but I doubt that it would try to annex all of Canada, there are too many people loyal to the British Empire who would see the annexation as an occupation.
The US would take the Bahamas, British West Indies, British Guyana, British Honduras, St Helena, the Falklands, South Georgia and the South Sandwich Islands, Bermuda, the Maritime provinces, Newfoundland, British Colombia up to the 52nd parallel, and British North Borneo and Sarawak. The US would probably want some sort of British territory(ies) on the east Atlantic as naval bases. Likely Gambia, Sierra Leone, or maybe even Gibraltar.
Quebec would be established as an independent republic. It would be loyal to the United States.
The Spanish American war could play out...differently, but I'd think that with the Roosevelt Presidency the US and British Empires could come to a point of reconciliation, especially considering trade between the two is so important, and a strategic alliance would benefit both.