The official end of the war was a return to status quo. No territory changed hands between the British Empire and the United States. As a Canadian I also always learned that we won, which is both true and not true depending on perspective. Because Canada was the access point that the United States used to attack Britain, and the American invasion was repelled, from the standpoint of a Canadian (or rather Upper Canadian) the United States was defeated. From the point of view of Great Britain, the war was not much more than a footnote in the greater context of the Napoleonic Wars. Therefore, most likely to Brits at the time it was a nuisance that was dealt with, no real reason to discuss victory or defeat.

The Americans however, still have a lot of grounds to say they won the war. The war was declared in the first place as a response of the British not respecting American neutrality and stopping American merchant shipping. The war asserted United States sovereignty and made the Great Britian take her more seriously than it had. Furthermore, the United States left the war with a much more well organized and trained army and navy than they entered with. The war was a large factor in breaking the power of the Indian tribes opening the possibility of faster westward expansion and unified the states under a more strongly centralized nation. Finally, the victory over the British at the Battle of New Orleans was a source of national pride and further unification.

TLDR. depends on your perspective and what you value as the result of the war