There is also the theory that the British just had more practice at gunnery and sailhandling while blockading the French/Spanish in the various ports.
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The Americans drilled daily with live cannon, while the British drilled less often, and without live fire (presumably to conserve powder and balls).
As an unsurprising result, American crews were more experienced at reloading under the duress of cannonade. The sound on the gun decks was so great it would burst eardrums. The smoke made it too hard to see anything a few feet from the portals.
If you've never been near a gunpowder cannon fire, it's hard to comprehend the surreal rupture of reality it causes in your perception. I was to the side, but in front, of one. My world went black, then lightening values of gray. Sound returned. Then people appeared in the fog, moving with their arms out trying to get away blindly from the threat they perceived (that was already over).
Without proper training, new sailors will stumble badly in their first firefight, and each man on the gundeck is crucial to a team. The officers were outside the deck, so they could receive orders. If you can't load your cannon while blind and deaf, your cannon sits quiet a long time.
I'm pretty sure the effect comes from the sound and not something like toxic gasses because I never get the feeling shooting smaller calibers, nor do I get it when shooting with a silencer. It's too bad silencers are so restricted in the US. I think a lot of shooters would be in better health if they were more common.
We're instructed to exhale before firing because the concussion of the round leaving the front while its propellent leaves the back of the tube creates a brief vacuum. If you don't exhale, the air is forced out of your lungs so violently you feel like you got punched in the chest.
The noise is undoubtedly part of it, but the atmospheric effect is not insignificant, I think.
Yeah that's exactly why indoor ranges kind of suck for any serious rifle caliber.