Good points, Teribus. I think the long range factor was important in the encounter between Renown and Scharnhorst & Gneisenau. Those German ships, however, were not "heavy cruisers". They were somewhat undergunned high-speed battleships or perhaps you could call them battlecruisers. A main armament of nine 11" guns (in 3 triple turrets) was a far heavier armament than any heavy cruiser carried. A heavy cruiser in those times was a ship mounting six to ten 8" guns. The most typical heavy cruiser armament at the time was eight 8" guns in 4 double-barreled turrets. This was true of the German and British heavy cruisers of the day, such as the German Hipper class or the British County class cruisers. (The British also had a smaller class of heavy cruiser in service, such as the Exeter, with six 8" guns.) Japanese heavy cruisers usually carried ten 8" guns, American heavy cruisers usually carried nine.

The 11" gun was a battleship caliber gun, but very much to the lighter side by WWII standards. It was a smaller caliber gun than should have ever been mounted on ships such as Scharnhorst and Gneisenau. I'm sure that at extreme range this would have presented problems in facing Renown's eight 15" guns, as you suggest.

On the other hand, Scharnhorst and Gneisenau were very fast ships, and they had a total of eighteen 11" guns to bring to bear on the Renown. They were also more modern and better protected than the Renown. I think if the Germans had been in an aggressive mood that day, they might well have decided to close on the Renown and fight it out, in which case they could well have sunk her, though at the risk of considerable damage to themselves.

Evidently, they were keeping on the cautious side, and they decided to use their speed to disengage. The German Navy was generally quite cautious about engaging British heavy units, because the Germans were badly outnumbered in the war at sea and could not afford equal losses. On top of that, they were given orders to be overcautious, because Hitler couldn't stand to risk or lose big ships. This negative attitude on Hitler's part hampered the big German ships again and again in the naval war with Great Britain, and it only delayed their inevitable loss and made their lives miserable in the interim. Hitler was a dreadfully bad person to put in overall command of a naval war...he himself had asserted that on land he was courageous, but at sea he was a coward! Not a good psychological situation for the German Navy.

Only the heavy cruiser Prinz Eugen survived the war in fighting condition. All the other large German ships were sunk or ruined beyond repair (some by being bombed in harbour by the RAF).

Isn't it fun talking naval minutiae? ;-) I know I'm enjoying it.