TNG itself was unable to come up with a better story than BOBW. "I, Borg" and "Descent" were the only Borg stories afterwards and neither were that good.
VOY didn't choose a "safer story" with the Borg, there just wasn't any way to tell a more "extreme" story in the first place. They couldn't up the ante from BOBW since they were in the Delta Quadrant and not home, and no one would give a damn if they had a story about VOY saving the DQ from the Borg.
No, the TNG writers themselves came up with the idea that the Borg were from the Delta Quadrant. They invented the Transwarp conduits and gave the Borg superior travel power. They KNEW the Borg could travel fast already, they mention it in BOBW! The TNG writers KNEW they had this tech back in TNG and just did nothing with it, hoping no one would notice or call them on it. They got lucky and VOY didn't.
Like I said, TNG overpowered the Borg too much and did too little to wrap up this plot point.