I ought to emphasize that I haven't built either of these kits, or seen them first-hand. So the following is all based on the literature from the manufacturers, the photos in the ads, and a general familiarity with kits of this type.
To begin with, the appearance of any ship model built from a wood kit depends, to an enormous degree, on the builder. Two models built by two people from the same kit are going to look a lot different. Most of the wood ship model kits on the market (like most of the plastic ship model kits on the market) are, in terms of their resemblance to real ships, trash. But Model Shipways and Bluejacket are two of the finest wood kit manufacturers in the world, and their respective Constitution kits are among their more recent and sophisticated kits. The Model Shipways one is a little more recent; it's pretty clear that the company intended it as competition for the Bluejacket kit. But I'm sure both are excellent.
There are a couple of conspicuous differences. The Model Shipways kit is on a slightly larger scale, and the two kits represent the ship at different points in her career. The MS kit, from what I can tell, tries (quite successfully) to replicate what she looks like right now, as preserved at Boston. The Bluejacket kit represents a major research effort to determine what she looked like during the War of 1812. (There's quite a bit of room for disagreement about that; if you do a search you'll find several threads in this Forum that discuss the issue.)
I'm confident that either of these kits, in the hands of an experienced modeler willing to devote several years of his/her spare time to it, has the potential to produce a beautiful, accurate model. (The old Revell kit also has that potential.)
One other point struck me when I looked up the MS kit on the Model Expo website (www.modelexpoonline.com) a few minutes ago. (Model Expo owns Model Shipways, and functions as the Model Shipways distributor as well as a retail outlet.) Model Expo currently has 17 Constitution kits in stock - more than most of the other kits in the Model Shipways line. These kits are produced, and sold, in numbers that, by the standards of the plastic kit industry, are incredibly small. (Plastic kit production runs number in the thousands - at least.) And, as anybody who's ever worked in a hobby shop knows, only a very small percentage of the sophisticated wood ship model kits ever gets finished. (Actually that's a common phenomenon among model kits in general, but the wood sailing ship kits are the worst. The second-worst are the balsa-and-tissue airplane kits.) Far too many people buy these big ship kits without having any idea what they're getting into.
In my long-ago days as a hobby shop employee I always advised newcomers to start with a small ship in a large scale - something that can be done in a few weeks or a couple of months. Most customers, of course, ignored me; everybody wants a Constitution, Victory, or Cutty Sark. I sold plenty of those big kits to newcomers, virtually none of whom I ever saw again. (The reputable manufacturers understand this problem. Both MS and Bluejacket emphasize in their literature that their Constitution kits are for experienced modelers.)
When those enthusiastic newcomers get home and started their kits, at least one of several things usually happens. In some cases, the contents of the box, and the vagueness of the instructions (which are written for modelers who have lots of experience under their belts), are so intimidating that the kit gets stuck in a closet and forgotten. If the newcomer does work up the gumption to start the model, he/she often gets discouraged at the amount of time it takes to make even a little progress on it. Just as frequently, he/she works on the model for several months and then discovers his/her skills have improved during that time, with the result that the work completed a couple of months earlier no longer looks satisfactory. That can indeed be pretty discouraging.
As anybody who's read my rants in this Forum probably has figured out, I'm a big believer in plastic kits. I have to acknowledge, though, that the wood kit market - though most of the kits in it are overpriced garbage - has one big feature to recommend it over the plastic kit market: a considerable number of good, well-designed, accurate kits that can be completed successfully in a reasonable amount of time by newcomers. I'd suggest that anybody interested in getting into wood sailing ships take a good look at the "Group Build" forum thread that's currently discussing the Model Shipways Sultana. That's a fine kit that doesn't take years to build, isn't extravagantly expensive, and turns into a mighty handsome model. A few weeks spent on a model like that will be an extremely sound investment when the modeler tackles something more sophisticated.