No arguing the historical significance for the U.S. and Canada, but my understanding is that if the British hadn't had badder fish to fry, they probably would have mopped the floor with us eventually.
At least, that's what I've gleaned from some fairly casual looking and one conversation with a history professor since last year when I saw that dreadful documentary. I'm no expert. Like most of the country, I was given little more in history class than "we fought the British again in 1812" and didn't pursue it much until just recently. You certainly are better informed than I, so don't be shy about correcting me further if my broad sweeps are a bit too broad.