Which is interesting in another way, because it implies that the Borg ship that attacked Earth in "First Contact" was completely unrelated to the one that attacked them in "Best of Both Worlds."Doesn't the episode imply the 2063 borg are the reason the borg are heading to the Beta quadrant?
The estimation of how long it would take for the message to reach the Delta Quadrant is the 24th century.
First Contact implies that Picard had been assimilated by the Borg before, but it strongly implies that the Borg Queen had always been present on that ship and had worked closely with Picard on its mission. This vaguely implies a version of the Borg invasion slightly different from "Best of Both Worlds" in which Locutus wasn't actually all that important and may have just been one of hundreds of officers assimilated in a prior incident.
Picard says "They attack our space, and we fall back... they assimilate entire worlds, and we fall back..." This, too, paints a vision of Federation/Borg interaction COMPLETELY different from the prime universe, since the Borg attacks we've seen didn't involve them "assimilat[ing] entire worlds" or the Federation falling back in the face of that threat. Even in "Best of Both Worlds" they went out of their way to engage them as quickly as possible.
Lastly, the Borg's M.O. changes completely in First Contact and they are using COMPLETELY different technology as the last time we see them. Where as in TNG we have Hugh saying explicitly "The Borg assimilate civilizations, not individuals." In First Contact, not only are they content to assimilate the Enterprise crew literally one at a time, but they also travel back in time to prevent humanity from ever developing useful technology, which would, supposedly, make them that much easier to assimilate.
In the end, we're forced to speculate (in universe, at least) that either there are two different timelines, or two VERY different versions or species of the Borg.