Radar fire control gives three Des Moines cruisers the edge

Who would win between Scharnhorst and Gneisenau and three Des Moines-class cruisers?

The Des Moines group is favored, decisively at night and probably by concentrated radar-directed rapid fire in daylight despite the German ships' heavier armour.

At night, the radar-equipped Des Moines-class cruisers are expected to dominate because they can find and hit the German ships before receiving effective return fire. In daylight, Scharnhorst and Gneisenau gain a better chance through heavier protection and damaging 11-inch shells. The American advantage remains the rapid, radar-directed volume of 8-inch fire from three ships, allowing two cruisers to concentrate on one target while the third engages the other. The answer treats first effective salvos and fire distribution as more decisive than a simple comparison of gun calibre.