Alaska versus Scharnhorst in a gun duel

Which would usually win a gun duel between Alaska and Scharnhorst?

Alaska is tentatively favoured for a possible range advantage and more effective radar-directed fire. Both ships had radar.

Clarke tentatively favours Alaska, recalling a possible range advantage and expecting earlier effective fire. Another participant points out that both ships have radar-directed gunnery. That qualification is accepted, though Alaska's system is still judged better. Scharnhorst's fighting against British cruisers at North Cape illustrates the distinction between having radar and obtaining effective results.