Gneisenau vs. Strasbourg

Goes to show how much luck can play a part in naval battle. Renown hit by 2 x 11in (I thought that they were 5.9 but no matter, happy to be corrcted) and no real damage. Germans hit by 1 x 15in that knocked out the Fire Control (it might have been repaired, but it must have been a nasty moment and taken time to fix) and a 4.5 that takes out the rangefinder on a main turret. You could probably fire a 4.5 all day at the Gneisenau and in normal circumstances not hit anything important.

Yep. Luck is the big one unknown moment. I also have no knowledge what was hit on Renown (maybe someone can help out, please?) but I suspect it wasn´t that important.
KM ships have a bad reputation for loosing their FC soon in a prolonged battle:
Bismarck during her last battle (it was the first or second salvo to hit the ship and subsequently knocked out Main FC, forward FC, turret A and B and rear FC...what a hell of luck!)
Scharnhorst during north cape (against Sheffield and Jamaica it lost it´s forward FC, on the other side Duke of Yorck suffered just the same hit which suffered Gneisenau in 1940 by Renown: a 11" hit penetrated the upper superstructure, cutting the radar FC cables and detonating outside. Killing a few FC crew. As for Gneisenau, the damage crews could fix the cables later and resume FC operations sucesfully)
The biggest disadvantage of the twins was their weak deck protection. On the other side no ship to sail the seas ever was that immune to belt penetrations (including Bismarck). It´s 350 mm KC main belt and 105 mm Wh sloped plus 45 mm Ww torpedo bulkhead made penetrations completely impossible for all ever build guns. This is unnecessary overarmor, realized by the designers. The Bismarck had 320mm KC and 100mm+ 45 mm and still was immune to all belt penetrations (except fora tiny cahnce of a brand new 18.1" at 0 distance and direct impact angle), Tirpitz belt was lowered to 315 mm KC+100mm+45mm ad still enjoyed almost impenetrability (except Yamato at 0 yrds). The H-clss even furtherly reduced the belt to 300 mm + 105mm + 45mm and even this thin belt implies immunity against all allied guns.
Had Scharnhorst lowered it´s belt to 300 mm KC the weight saved could be used for beefing up the main deck armor to 80 mm for a significant weight reduction or even 95 mm without significant weight reduction. A BC needs to have good deck protecttion because it will usually dictate the terms of engagement (and disengagement) and doesn´t want to stay in the battleline at closest distance.
From this point of view the Dunkerque (as KGV) were much more belanced designs than were the twins.