Reading the lyrics of the two songs, I don't believe that the Crimson King would bother himself with a fight.
He seems instead to be a passive, inscrutable figure who holds court to various characters each engaged in their own opaque, elliptical schemes, as all the while The Crimson King looks down upon these self-defeating machinations with a melancholic, fatalistic gaze.
A better, more even battle would be between News of the World Robot vs. The 21st Century Schizoid Man.
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Disprove the return of a potato (5)