That's a very debatable proposition. Canadians consider it a Canadian victory. The British don't really think about it at all--it was a minor sideshow to the Napoleonic Wars. Most historians consider it a draw, since nothing really changed from before the war.
The War of 1812 was significant because the Brits accepted US independence and the Louisiana Purchase, both of which would have been in jeopardy had they won the Battle of New Orleans.
Yes, the British considered their victory over Napoleon to be decisive. They put the old Royals back in power in Europe. However, that did not last very long.