How would an Alaska-class cruiser fare against Scharnhorst?

How would the Alaska class fare against a Scharnhorst-class battleship?

Roughly even odds if Alaska uses speed and fire control to engage one ship at a time; Scharnhorst remains more robustly subdivided.

The Alaska class benefits from excellent fire control, effective 12-inch guns, and speed. Scharnhorst retains a major advantage in subdivision and battleship-grade resilience. On this reading, Alaska has roughly even odds only when she can use maneuver and convoy geometry to avoid fighting both German ships together. The comparison turns on engagement control and survivability rather than caliber alone.