The original 3 big American frigates mounted 24pdrs, while most other nations' frigates had 18pdrs. The sides (scantlings) of the American frigates were also stronger, so that shot fired at long range from 18pdrs failed to penetrate. The proportion of long guns to carronades on American and British frigates was about the same. There was a plan on the American frigates to place carronades on the spar deck (between the forecastle and the quarterdeck) but this wasn't often done in practice because it affected the sailing qualities.

To counter these the Royal Navy had several 24pdr ships - Endymion, Cambrian, Surveillante (ex-French), which were quite a bit smaller. They quickly built others in 1813-14 (in fir); 5 repeats of Endymion, and the larger Newcastle and Java, which were similar in size to the Humphries design.

Indefatigable and Magnamine had been cut down from 64gun ships-of-the-line in 1795, carrying 24pdrs on the upper deck, but without the heavy carronade armament of the American vessels. Goliath, Saturn and Majestic were cut down from 74s in 1813, and carried 32pdrs.
Endymion and Saturn were part of the squadron that captured USS President in 1815.

Returning to the Rose (the ship used in the film for HMS Surprise), Rose is a somewhat inaccurate replica of HMS Rose, a 20gun sixth rate ('post-ship') built in 1757. Actually HMS Rose was built at Blaydes' shipyard here in Hull, less than half a mile from me, and only a few yards from where Bounty was built.