Someone said that they include mostly experimental freaks and museum ships. He points out to various "transwarp" projects and even a Constitution.
The model of a Connie found at W359 is the same exact model of the destroyed Enterprise used in ST III. Personally, I want to kick the balls of the idoit who thought it would be funny or wise to put it in there.
Someone said it was a museum ship, possibly the Enterprise-A. I however, disagree. If the Enterprise-A is converted in a manner similar to, say, the USS Nautilus (a vessel I have actually been on as a museum ship), then it will be next to impossible to refit her for serive, let alone on such short notice. Much of the structure would have been converted to best suit any visitors, equipment would have been modified or removed to accomodate visitors, and almost certainly the warp core would have been removed, and most likely scrapped or possibly used in another vessel. The Nautilus would be a perfect anology, since its nuke plant had been removed and disposed of for safety reasons, and surely the same would apply to a warp plant as well. To put it short, it's simply impossible.
As to how a Connie ended up there, well - that's why I want to kick the balls of the idoit who put it there. I think the best theory is that it was one of the last ships of that line to be decommissioned, and it was still in the mothball fleet, possibly only months or even days away from pernament disposal. This still could be the Enterprise-A, still awaiting conversion to a museum ship, but I hate to think of a ST ship I actually like being lost! As to "Relics," since Picard states that the "only Constitution left" is in a museum, we'll just have to assume he's mistaken. Considering that this is Picard we are talking about, that's an easy concession to accept

As to the Excelsior study models, there is reason to both believe that they were experimental models in the Transwarp project pulled from mothballs, or we can except the fact that they are represenitives of full production starships, that may even still be in service. I believe one can easily believe both, and there is no evidence that I am aware of to support only one of these theories. I suppose it depends on personal interpretation.
As for the other models, I suppose its also interprable. I personally am inclined to believe that at least the New Orleans represents a full production model.