Britain as far as I can tell had no interest in re-conquering the old American colonies, only in defending Canada (again, the crucial point here is that Britain absolutely did not want to fight a war with the US and tried to avoid it through diplomacy). Britain successfully repelled the American invasion of her territory and took the war to US territory instead.
Based on the initial war aims of both sides, Britain won the war. America at best mitigated what could have been a completely disastrous mistake on their part to declare war on Britain. Calling the war of 1812 a US victory requires a truly impressive level of cognitive gymnastics to genuinely believe when taking in all of the evidence, otherwise you’re just looking at the Battle of New Orleans etc and ignoring the overall strategic picture.
Not that it matters, but the US didn’t even win the last land battle of the War, which was the Second Battle of Fort Bowyer, in which the Americans lost almost as many troops (mostly as POWs) as the British had seen killed in the Battle of New Orleans, as well as about 22 captured artillery pieces...
I’m not going to let your facts distort my delusions. The war was a victory because 20 years after gaining our independence we kept it; Britain ended up with Britain, and we ended up with the United States. I’m sure every British soldier that fought in North America was pondering that as they sailed back to their rainy, foggy island (or worse, had to stay in Canada). Well, at least they hung on to Bermuda...