Been a while since I saw the movie... I thought the story was that the Acheron was so much stronger it was a ship of the line.
The Surprise was an aging 28-gun frigate, the Acheron a new, 44-gun one. It was armed with 18-pounders IIRC, as opposed to the Surprise's 9-pounders, thus throwing considerably more metal with each broadside. The fact that frigates grew around the start of the 19th century and that the Surprise was somewhat aging ("would you call ME an aging man-of-war, doctor?"

), is often made a point of in the novels. Even Jack Aubrey doubts he could take on one of the new 38-gun American frigates in the Surprise, but mostly because she wasn't built to take the guns that would be required to attack one. Yet he still loves his ship, and indeed takes it yardarm to yardarm with a French 74 in the Indian Ocean in "HMS Surprise", the third novel, actually managing to inflict some damage, and getting away because of the superior sailing qualities of his ship.
That is one of the things I love so much about O'Brian's books; the descriptions of how Aubrey loves the Surprise, and is able to bring out the best of its sailing qualities, often outrunning much larger and more powerful ships.