...Or then the partial Constitution at Wolf 359 was a museum specimen dragged out for this final battle, much like "Unification" suggests one can quickly reactivate and warp out a mothballed starship (and like Sternbach and Okuda suggest the Constellations are preserved as "activatable" museum pieces). Probably a very expensive way to conserve ships for mere display, but the benefits may be almost worth it.
But it wasn't a "final battle." It was Starfleet's primary engagement of the Borg. The only reason why you would take a ship out of mothballs is as a last resort because all your other ships have been destroyed. That's not what happened here. Starfleet sent only 40 ships to stop the Borg, it was only one battle, and all ships were destroyed at roughly the same time. In retrospect, it seems that Starfleet didn't consider them to be that much of a threat if that's all they sent, since the fleet consists of possibly thousands of ships, any one of which could have been used before they resorted to taking an old ship out of a museum. For the Dominion War, maybe, but certainly not for the Wolf 359 engagement.
As for the Connie at Wolf 359, it's never been canonically shown that it was a Connie; we only see part of a wrecked saucer in one scene and part of a secondary hull in another. The two parts may not have belonged to the same ship or even belonged to the Constitution class at all.
And if you're referring to the Tripoli from "Unification," I was always under the impression that the Romulans or whoever was piloting that raider ship simply tractor beamed or just destroyed the ship before taking it's place, not that they reactivated it and flew it away.