Actually, if you look at the whole thing from a geopolitical point of view, although the British "won" the war, neither side really achieved its original war aims. In fact, the casus belli for the Americans (pressment of American sailors) wasn't even included in the articles of the Treaty of Ghent. The original war aims had got lost in the fog of war, rhetoric and poor communications.
What it all really proved was that the real cost of defending a country with a coastline as long as the US's was prohibitive given the communications and transportation available at the time. Similarly, the cost of attacking a country with a coastline as long as the US's was equally prohibitive. To win a territorial war, you must take and hold each piece of disputed territory. Neither side could do this in the War of 1812 - the Americans lacked the discipline necessary to achieve a successful invasion of Canada, and the British just really wanted the war to stop and were actually simply carrying out a police action. Their interests lay elsewhere at the time.
On the face of it, the Americans lost, hands down. At no time did they achieve their immediate battle aims in full, and they appeared to have no firm war aims at all. The Battle of New Orleans aside, they won few, if any, real and unequivocal victories, although the Indians fighting with them did. It cost a young country a bundle it could ill-afford for nothing other than a bit of national pride in return. Some say that it cemented the independence of the States, but that was pretty much a fait accompli by 1812 anyway, and I don't buy the argument.
FWIW.
