This was something they lost over the course of Voyager. Maybe it started earlier, I dunno. First Contact at least made defeating a cube difficult (and Voyager never did personally take down a cube), but I never really liked the idea of a Queen. It added a personal side to them which somehow makes them a touch more vulnerable.
The introduction of the Borg Queen was IMO a development that weakened the Borg as an antagonist. In Q Who and BOBW, the Borg were rather Hitchcockian villains: fear was driven by the characters talking about them as much as confronting them. Even Locutus didn't make them more approachable: he repeated the demands of the Collective without explaining them or seriously dialoguing with the Enterprise crew. Part of the appeal of this approach is that it made up for the lack of special effects to adequately portray the threat visually. I don't think Hugh and Descent changed that, as what we saw were elements that had become autonomous from the Borg as a socio-political entity. The Queen in ST:FC broke that spell. With a voice willing to reply directly to the Enterprise crew, much of the mystery disappeared. Their mentality and objective were laid bare in such a way that they could be objectivized and minimized.