While illegible in both episodes, this starship model was labeled as the USS Melbourne (NCC-62043).  An Excelsior-class starship was also named USS Melbourne in the "Emissary". This ship is listed as unnamed, because Memory Alpha considers the name of this ship has been retconned. See USS Melbourne for more information about the model and the naming issue.
Like the ship above, this was a reuse of the model labeled as the USS Melbourne.
The footage of this vessel in "Unification I" was a reuse of the footage from the Wolf 359 debris field from "The Best of Both Worlds, Part II", though the damaged sections of the hull were clearly on fire in the "Best of Both Worlds, Part II" version.
Initially the ship was disabled as it passed through a cloud of tetryon plasma, but later caught up with the Yellowstone and subsequently damaged the runabout's warp drive, causing the runabout's destruction. (VOY: "Non Sequitur")
Though from an alternate timeline, this ship most likely existed in the normal timeline.
In late-2372 of an alternate timeline this Nebula-class starship docked at Deep Space 9's upper pylon, when Starfleet decided to leave DS9 and the station was taken over by the Klingons. (DS9: "The Visitor")
Although not identified visually, it is possible that this ship is the otherwise-mentioned USS Lexington, which was referenced in comm chatter during the engagement.
On the other hand, it is concurrently possible that this ship was the USS Endeavour (NCC-71805), as per the Star Trek Encyclopedia (3rd ed, p. 135). In a preliminary script draft for the film, dated 29 September 1995, an Endeavor was explicitly named as one of the starships engaged in the battle in scenes 10 , "PICARD: Signal the Endeavor to fall back. We'll cover them.", and 11, "The Endeavor moves off as the Borg FIRE at the Enterprise and BLASTS the saucer section." These references did not make it into the final cut, leaving the one Nebula-class vessel actually seen, unnamed. Some prints of Star Trek: First Contact do not include shots of this vessel.
This appearance marked the last time that use was made of the physical studio model as a production asset. With the exception of the USS Enterprise-E, all other Federation starships in the sequence where executed as CGI models. For further information on the model, see Nebula-class model.