In a shoot out, which would win?
Doubtless, at this range, there would be no winner.
But there were quite a few battles between ships equipped with these weapons in the Napoleonic wars, the first American civil war (the War of Independence), the 1812 war between Great Britain and the US, and many others.
The long gun, manned by 9-11 highly trained gun crew, fired a ball of 24lbs weight, up to 2000 yards, with some accuracy. The largest long guns mounted on the biggest battleships (like “Victory”) fired balls up to 42 lbs.
The carronade was operated by 4-6 men, and fired a ball in this case of 32 lbs, at three times the rate of a long gun, but with dismal accuracy beyond 500 yards. They were much less expensive to buy and operate, and very popular with the bean counters. Carronades fired balls up to 68 lbs.
Since most sea battles were fought at ranges much less than 500 yards, carronades were credited with many spectacular victories. The British were so impressed that they installed carronades in addition to the usual long gun armament, to increase the overall firepower of their ships, but later they replaced the long guns with carronades in some ships.
In the war of 1812 between the Brits and the US, while the Brits were simultaneously engaged in a life and death struggle with the Napoleon, they were often beaten by the newer and more powerful frigates of the small US navy. One factor cited is that the British ships had fewer and less powerful long guns, and partly because they had changed over to carronades. The US ships remained out of effective range of the British carronades while causing huge damage with their long guns.
The carronade was used by the British navy for only half a century, vs 3 centuries for long guns.
They were both replaced by guns which were rifled, fired explosive shells, and were breech loaded.
For a very detailed analysis of these weapons, including original results of British Admiralty trials and summaries of many sea battles, see Adrian Caruana’s book, “The History of English Sea Ordnance” Vol 2, 1997. If you can locate a copy. I found one at the State Library of Victoria.