How Hood might have fared against Scharnhorst and Gneisenau

How would Hood have fared against Scharnhorst and Gneisenau in Renown's place?

She might have driven them off with early 15-inch hits, but Renown's newer systems made those hits more likely.

Early 15-inch hits from Hood might have persuaded Scharnhorst and Gneisenau to withdraw, as Renown's hits did in the historical encounter. Hood was less likely to land the same early hits because Renown had recently emerged from a major reconstruction with more up-to-date systems. If the German ships had stood and fought, either British battlecruiser could have faced serious danger. The comparison therefore turns on fire-control readiness and the enemy's decision to disengage rather than gun caliber alone.