The photo in the link Big Jake gave us is the same one that's in the Model Expo catalog, illustrating the Model Shipways kit. I haven't seen it in person (the Constitution isn't high on the list of projects I want to tackle), but I think millard is right about it. It seems to represent the ship as she exists in Boston at the present time.
The restoration she underwent in 1927 was important, in that it saved her from the scrapheap - and caused the Navy to make some detailed measurements and draw up a set of plans for her. That project was not, however, done to the standards taken for granted today. The guy in charge of it was a regular Navy lieutenant (whose name escapes me), who seems to have been extremely conscientious but didn't have much formal training in history or the theory of ship restoration. (In fairness to him, scarcely anybody else at that time did either.) His job was to rip off the "roof" that had covered the Constitution's spar deck for some years while she was serving as a floating barracks, install a completely new set of spars, rigging, and sails, and make various other alterations so she would resemble a sailing frigate again. Model Shipways used to sell a booklet that was published by the Navy at the time, and which described in some detail how the process had been carried out. An example of how the lieutenant and his staff operated: they found several old sets of spar dimensions, so in building the new spars they took the average of all those numbers. Not the sort of thing that would be done today. When those folks got finished she looked more-or-less the way she'd looked in the 1830s, or thereabouts. Quite a bit different from how she'd looked during the War of 1812, and even more different from her "as launched" appearance. But that was how she looked when, in the thirties (I think), she made a long voyage down the east coast, through the Panama Canal, and up the west coast. She was towed by a Navy tug, and the sails were kept firmly furled to the yards throughout the trip. (All this is recounted in Capt. Tyrone Martin's excellent book, A Most Fortunate Ship.)
Since then the Constitution has undergone several other restorations, each of which, to my eye at least, has brought her a bit closer to her War of 1812 configuration. There still, however, are some significant differences. It looks to me like the individual who built the model in the Model Expo photo was trying to replicate her current configuration - and he or she did a good job of it. My own inclination would be to shoot for an earlier period, but that's a matter of personal taste. I imagine that the kit, being wood-and-metal, would be fairly easy to finish in any configuration the modeler wanted.
I have one question. How on earth did Big Jake get a graphic description of the process of entering the Nether Regions to appear in his post, whereas my oblique reference to a female donkey a few weeks back got electronically censored?