Why Scharnhorst should run from Rodney

Could Scharnhorst realistically defeat Rodney in a surface gun battle?

Not on favourable terms; Rodney's 16-inch guns and heavy armour make escape a better option for Scharnhorst than a close-range duel.

Scharnhorst cannot be expected to defeat Rodney casually in a gun action. Rodney combines 16-inch guns with armour thick enough to make closing the range dangerous for an eleven-inch-armed opponent. Fitting Scharnhorst with 15-inch guns would improve her chances of inflicting damage but would not give her comparable protection. The rational German use of speed is therefore to avoid the engagement rather than seek a battleship duel on Rodney's terms.