The US probably could have handled itself in a land war, and England would have dominated the naval war. The US would probably be able to seize the territory, but the British could sail up and down the east coast landing troops at will and pull out before American troops could amass. The results of a war over the Oregon Territory would probably wind up with the same possibilities as OTL with the same sort of likelihood. Very small chance that America would get it all, very small chance England would get it all, small chance that it would become an independent republic like Jefferson wanted, and a good chance that they'd come to a compromise along the same lines as the diplomatic solution.
The aftermath would be much more interesting though. The US would be much more interested in building up a more powerful navy, the South would have been upset at another war over Canada and even more unhappy over fighting over territory that would probably end up to not be slave holders. English and Canadian relations with the US would certainly sour and that'd increase the likelihood of them intervening in America's civil war (Whenever it happens). An extra war in the 19th century would also increase the populous' anti-militarism, which would make a civil war less popular in the north.
So even if America wins all of Columbia, it increases their chances of losing the Civil War.