Battle of New Orleans really falls into category of the underdog beating the favourite. (After the war was supposed to be over, but that was because they didn't have mobile phones and suchlike in those days. But it mustn have been frustrating for the winners - like putting the ball into the net and getting it disallowed, so it couldn't have any effect on the result.)

Those winners Little Hawk gave there might have been popular with at least some people, but they didn't really register when it came to songs and suchlike.

There are plenty of good songs about Napoleon in the traditions of the British Isles, centring on his defeats (and on the whole rather sympathetically), but I can't think of any about Wellington. Or Patton, MacArthur, Montgomery or the rest of the crew.

One of the few cases I can think of where, on the face of it, the victor is celebrated is that of Santy Anna - sung of as having "won the day" while "General Taylor ran away", which is of course the reverse of what actually happened.

It still seems to me that if your victory isn't an amazing surprise, or you don't get killed in the process of winning, you'll never make it as a song hero.