While USS Constitution was an uncommonly heavy frigate (the heaviest I could find) with her 21 inch thick hull planking and 50 broadside guns (30 24pd great guns and 20 32pd carronades) She, like all ships, was by no means unbeatable. She unarguably had an advantage over any british ship on the station by broadside weight but she was by no means faster as a ship. Having been successfully clean just before the outbreak of war and refitted again under Bainbridge during the war she would have had a significant advantage over the blockading squadron perpetually on station or running up and down to halifax for rapid provisions and no time for a real overhaul.
However time and again history has shown us that it does not always come down to broadside weight to determine an engagement the captains of engaging ships played a huge part in any out come and both Hull and William Bainbridge were notably competent seamen whereas for example Captain Dacres of Guerriere had been ashore for the 4 years prior to the command and had only one major action (and this was storming a fort) before.
I'm rambling terribly from my point which is if wind, condition of ship, skill of command and luck were to favour an opponent it is far from inconceivable that the ship itself could be taken by a much lighter ship. Were it for example to be demasted by a lucky or skilled shot it would be no better off than any other ship. In regards to the game I would be quite unhappy to see everyone bumming around in constitutions because it wouldn't reflect the period well at all and as Destraex mentioned in the OP they would certainly be a match for all but the heaviest ships especially if it is capable of the same speed as a lighter frigate.