I can comment on most, but not all of these kits. One big caveat: what follows is largely in the realm of personal opinion.
My next major project is going to be a generic Gloucester fishing schooner from about 1910, which I'm going to name after my father. (I've already built a generic tugboat named after my wife. I really enjoy the lack of restrictions in that sort of project.) Some years ago I bought the Bluejacket We're Here, and some months back, when the Model Shipways Elsie was on sale for about $50, I bought it too. My intention is to combine features of both kits.
Either of those wood kits has the potential to be turned into a first-rate model. If I had to pick one, though, it would be the MS one. It scores over the BJ one in two important respects: the machine-carved hull and the plans.
The Bluejacket hull is made from good, clear basswood, but the machine carving is, by comparison, pretty rough. My big criticism is that the bulwarks aren't anywhere near high enough. That means either gouging out the deck deeper or building up the bulwarks.
The BJ plans appear to be very old. One sheet, with the hull lines and sail plan crammed on it. And I think it's actually the plan that accompanied an old Bluenose kit. (The text blocks reading "We're Here" obviously were added later.) I think the hull probably came from that kit as well both it and the drawings look an awful lot like the Bluenose.
Model Shipways issued an Elsie kit many years ago, with decent plans and lead fittings. (If you find one in a classic MS yellow box, that's it.) Much more recently, MS released a complete redo of the kit, with britannia metal castings and a superb set of plans by Eric Ronnberg, the reigning expert on fishing schooner history. There are three sheets of plans, and they contain just about every detail that could possibly be crammed into a 1/96-scale model. If you want still more information, though, Ronnberg published a series of lengthy articles in the Nautical Research Journal. (if any serious scale ship modeler doesn't have a copy of the NRJ's back issue CDRs, I highly recommend it.) The MS hull is carved considerably cleaner than the BJ one - and the bulwarks are the right height.
The fittings sets for the two kits are pretty evenly matched. Bluejacket, of course, makes its blocks and deadeyes of britannia metal, whereas Model Shipways uses imported wood ones. (That, in itself, accounts for a big chunk of the price difference.) Which is preferable depends on the individual modeler. I personally like the metal ones, with cast beckets, for this particular kind of model, but the MS wood deadeyes are beautiful and the blocks aren't bad. Bluejacket includes a small fret of photo-etched brass, including the bow ornamentation, the skylight, and two companionway doors. Very nice.
The bad news is that, at least for the moment, Model Expo has discontinued the Elsie kit. I read a news item recently to the effect that it will be brought back in the plank-on-bulkhead format. (I have the impression that Model Expo is moving away from the machine-carved hull.) The plans, however, are still available - at a reasonable price. Also highly recommended.
The Model Shipways Roger B. Taney is a very, very old kit. I think it was originally released in the late 1940s. It was based on the plans in Howard I. Chapelle's History of American Sailing Ships. Those plans were sort of generic, covering the entire Morris class of revenue cutters. Some years after that, Chapelle located another contemporary set of drawings specifically of the Taney. He published his version of those plans in The History of the American Sailing Navy. They're different in some noticeable respects from the earlier version - which MS used. If I were building a model from the MS kit, I'd call it one of the other ships of the class.
Some months back Model Expo announced that it was bringing the Taney kit back, but that hasn't happened. I suspect that if it does, the kit will be plank-on-bulkhead. If you run across an original, yellow-box version, it will have the original cast lead fittings.
The Lindberg, ex-Pyro Elsie is a much smaller kit, originally part of Pyro's $1.00 series of sailing ships. I don't recall having seen this one in the flesh, but the whole series was characterized by highly simplified detail, overdone wood grain, and injection-molded "sails" with the spars cast integrally. I question whether building a serious scale model from that kit would be any easier than starting from scratch.
Pyro also used to make a model of the fishing schooner Gertrude L. Thebaud on 1/96 scale. It was later reissued under the ridiculous label "American Cup Racer." (Fishing schooners like the Thebaud, Elsie, and Bluenose did sail memorable races with each other, but the implication that that kit has something to do with the America's Cup is pure fiction. An America's Cup racer with stacks of dories on its deck. Yeah, right.)
That one was pirated from the Marine Models Thebaud kit. It was one of the very first plastic sailing ship kit, and was pretty simple but reasonably accurate. It can be turned into an extremely handsome model. Back in 2006 one of our Forum members built such a model, and provided some excellent in-progress photos of it: http://cs.finescale.com/fsm/modeling_subjects/f/7/p/53696/682589.aspx#682589 .
My biggest reservation about that kit is that, though my memory of it is pretty sketchy now, I think Pyro may have left off the stem- and sternposts from the one-piece styrene hull. If I'm right, it wouldn't be too difficult to add them. I can recommend the kit with those reservations.
The Lindberg "Independence War Schooner" is a reissue of the Pyro Roger B. Taney, which was pirated from the old Model Shipways kit. (The two gents who founded Model Shipways referred to Pyro as "Pirate Plastics.") We've talked about this one several times here in the Forum; a search on the name "Taney" should bring up some useful comments. In brief, it appeared at about the same time as the Pyro Thebaud kit, and shared many of the same characteristics: sound basic shapes and simplified details, but not bad. (One odd thing I do remember about it: most of the gunports were molded closed, with their edges represented by raised lines. And the lines on the insides and outsides of the bulwarks didn't line up.) Again, a good, solid start to a nice model - but I'd call it a different member of the Morris class. (At least one of them wound up in the "Texas Navy" during the Texas War of Independence, so the later label isn't exactly incorrect.)
If I were thinking about such a project, though, the kit I'd look into would be the Alexander Hamilton from Cottage Industry Models ( http://cottageindustrymodels.com/?page_id=95 ). I saw this one at an IPMS convention a few years back, and it looked excellent. The hull is cast resin, the fittings are cast metal, and the spars are wood. I haven't bought it, but it certainly looks like a fine kit - with an unusual but sensible approach to materials.
If I had to rank the four kits in order, I'd say: 1. Model Shipways Elsie. 2. Bluejacket We're Here. 3. Lindberg "War of Independence Schooner." 4. Lindberg Elsie (which, frankly, I wouldn't buy at all.) But I think that Cottage Industries kit belongs near the top of the list - and the Pyro/Lindberg Thebaud should be on it.
That's about all I can offer. Hope it helps a little.