The anthem does not appear to me to be a bravery comparison, altho I can see it might be considered by some to be implied. That's never been an issue for me. I know of no research which would show that Americans are more brave than people of other countries, but does the anthem state they are?
My main beef with the anthem is that it glorifies war. Should the prime thing we be proud of be our proclivity to warring? I don't think so (I actually think it's the primary thing we need to change). And the War of 1812? The reasons and objectives were a very mixed bag. There were some legitimate grievances, but one must note (and this point was made in the official film when I visited Fort McHenry decades ago) that it also was a war of aggression.