For the most part, the "basics" of the ships represented in POTC (given your time period) are ~fairly~ accurate. Wooden ships took an awfully long time to build, and hence their life/service spans were equally impressive. Some wooden `ships-of`-`the-line`, for instance, served for centuries, whilst others lasted less than a decade due to the chronic production flaws which were so common due to the primitive means of ship "modelling" available during these early years of `ship-design`.
Like "galleon", however, the word "frigate" actually refers to (for the time) a very broad range of ships. In actually history, for instance, the "corvette" as represented in POTC would actually have been a lesser class of frigate - frigates ranging from `single-deck` 20 gun ships to 48 gun `double-deckers`.
Other than that, the ships of POTC are `more-or`-less acceptably rendered - although it would have been very nice to see second and `third-rate` `ships-of`-`the-line` as opposed to just the 100 gun `man-of`-war, which personally I find looks rather odd without its appropriate support.
It would be logical to assume that the "battleship" is merely an older "war galleon", a ship still formidable but rendered obsolete in the era of `100-gun` `first-rates`.
In terms of firepower, English culverins were forged using `age-old` `bronze-working` techniques whilst the French cannon was typically made of iron. Bronze cast culverins were typically a far more expensive weapon, but the malleability of the material provided increased safety (as the cannon barrel, cast of brittle iron, was prone to exploding), and reduced recoil (hence, faster reloading) and more concentrated forward thrust (increased range and muzzle velocity). This weapon thus gave the English a devastating advantage over the Spanish and French throughout the colonial years, resulting in a margin of potential `sea-borne` carnage that was only deepened by the French reliance on `two-wheeled` and even skidded (mounted on iron "skis") gun carriages.
This aspect of naval warfare is certainly ~not~ well rendered in POTC, as the early English proved all too well that `twice-as`-important to gun caliber was the quality of the gun crew and the metallurgical science behind the weapon itself. In addition, no ship ever relied solely on any "single" class of gun. Even the coveted H.M.S. Victory (Horatio Nelson's flagship - a 100 gun `man-of`-war - at the Battle of Trafalgar) carried `32-pound` guns only on its third deck, the second housing `24-pounders`, the first `16-pounders`, and on the top - any combination of `12-pounders`, mortars, and cannonades (or, "murderers", as they were more popularly known).
Personally, I would think it very cool myself if such "`fine-tuning`" of `gun-power` were added to future builds. Hope this helps.
P.S.: In regards to gun carriages, the English were very quick to mount even their heavy `32-pounders` on sturdy, `iron-reinforced`, `four-wheeled` carriages. This enabled them to ~utilize~ the gun's recoil as part of their reloading procedure, and to maintain a most punishing `rate-of`-fire.