Who would win?

I guess even if the Death Star were able to destroy a single Borg Cube, that would be it at most.

So all the Borg needs is a superstar flyboy hero type in a little one manned spacecraft with a little energetic torpedo to fly an impossible space battle against thousands of TIE fighters, fire his way to the Death Stars surface, fire his torpedo in an exact location and blow up the entire thing on his own.

If you go by the screenshots of the movie when it shot Alderaan, the laser blast would envelope the entire cube.