Does the Death Star have a large compliment of Tie Fighters n'stuff? If it does, then, the Death Star wins.
If not, then the Borg Cube very slowly maneuvers, at all times, outside of the superlaser and the other guns.
As has been shown in otherthreads, the Star Wars weapons have a much shorter range than the Star Trek ones. The Borg Cube can sit, quite comfortably outside of all fire from the Death Star, and scan the Death Star for weaknesses. Then teleport torpedoes inside the ship's weak spots.
The Tie Fighters will change this, though, IMO. They should quickly be able to destroy, by swarming, one Borg cube before it adapts.