I recently visited the Vasamuseet in Stockholm (great museum, by the way!) and learned all about the Vasa, which was essentially the crown jewel of warship technology at the time of its construction in 1628. (Except in the "staying afloat long enough to leave the harbour" sense.) It got me thinking about technological developments during the Age of Sail.
The technological asymmetry between a modern warship and a frigate like the Constitution doesn't require much elaboration. A modern ship is faster, possesses much more firepower, and is so well armored as to be effectively impervious to the Constitution's armaments. This is because it has engines where the Constitution has only sail, modern guns where the Constitution has cannon, and steel armor where the Constitution just has wood.
Comparing the Vasa to the Constitution, however, I realized that I don't know what technological developments separate the two. They're both made of thick oak, are powered by sail, and field heavy cannon. Given the 170 years between the two, the Constitution would kind of have to come out the victor, but I don't know if the victory would be as lopsided as the hypothetical battle between the frigate and a modern ship. Hence my question. How did warship construction, battle tactics, armaments, etc. advance between ~1600 and ~1800? Did the paradigm change as much as it did between ~1800 and ~2000? To what extent would the Constitution outmatch a ship of roughly two centuries prior, and what would be the deciding factors?
(Note that while I'm referencing the Vasa, an answer by no means has to be restricted to that ship, as it's just one that I saw recently.)
This kind of thought experiment can be fun, but in this case, well, there's really not a comparison between the two ships. Just looking at the size of the two ships, their number of guns and number of crew suggests the Vasa would be badly overmatched:
Vasa: Weight (displacement) approx. 1200 tons; complement 145 sailors and 300 soldiers; main armament 48 24-pounder cannon, with a smattering of swivel guns and six howitzers; length 155 feet between perpendiculars; 13,000-odd square feet of sail.
Constitution: weight 2200 tons; complement 450, including 55 Marines; main armament 32 24-lb long cannon and 20 32-lb carronades; 42,000 square feet of sail.
So in Constitution you have a more heavily built ship, with a bigger crew, more and heavier guns, carrying more sail. Assuming an equal level of crew training and officer skill (and assuming Vasa magically solves its stability problem): unless Vasa catches the other ship off guard, it will be a long short day for its crew.
The way I would assume an engagement would go is that Constitution would use its better speed and sailing qualities to gain the weather gauge (an upwind position from the Vasa) so it could dictate the engagement. The Constitution's 24-lb guns would be longer ranged than Vasa's, so it would be able to stand off and fire on the Swedish ship until it was disabled, then close to finish the job with its heavy but short-ranged carronades. (The carronade was a British invention of the late 18th century -- a light gun with a short barrel that fired an enormous ball at low velocity for a massive smashing effect.)
Now with that all said, it's worth pointing out that Constitution and its sisters President and United States were explicitly built to be large, heavily armed frigates -- the term "pocket battleship" gets thrown around to describe them, but they were built to be larger and more heavily armed than contemporary RN frigates.
Some posts of mine that might offer you some more information:
https://www.reddit.com/r/AskHistorians/comments/2709jm/how_would_a_britishhms_frigate_built_in_1715/
https://www.reddit.com/r/AskHistorians/comments/2fs8qr/how_much_more_advanced_was_a_british/
That last answer talks somewhat about the building of the original six frigates of the U.S. navy, in particular why Chesapeake was such a mess.
Please let me know if you have follow-up questions!
One thing I haven't seen discussed yet is that the period of ~1600 - ~1630 saw a transition in gunnery, so while the basic broadside method of the Wasa would not be extremely different from the Constitution two centuries later, it was very different from what was practiced just a generation before. The main difference? Cannons around 1600 and earlier did not use a recoil method to reload, making the reloading process much slower since the gun crews had to pull the cannons back by hand. This encouraged hit and run tactics, with ships darting in to discharge their guns and pulling away to reload. This is also one of several reasons why guns were primarily mounted at the bow and stern, since they could be fired at the enemy both while moving forward and moving away.
Advances in metallurgy around 1600 made cannons more reliable and lighter (one reason for heavy guns before was that they were less susceptible to bursting). Lighter guns were more susceptible to recoil, and that recoil was turned to the gun crews' advantage. It's not entirely clear when the transition to recoil gunnery began, but the Spanish Armada in 1588 was fought with hit and run tactics and fixed guns while by 1630 recoil gunnery and broadsides seem to be the norm.
The end result? A fight between Constitution and a ship just a few years before Wasa would see the ship from the 1800s have a significant advantage in rate of fire, alongside all the other advances discussed elsewhere in the comments.
Source is The Safeguard of the Sea by N.A.M. Rodgers.
I asked a similar question a while back. You may want to also check out that thread.
Interesting answers by /u/white_light-king, /u/jschooltiger and /u/Notamacropus
https://www.reddit.com/r/AskHistorians/comments/2fs8qr/how_much_more_advanced_was_a_british/