The German Battlecruisers had the same guns as the equivalent battleship.
So 11 inch guns on Von Der Tann and 11 inch on Nassau.
12 inch on Derfflinger and 12 inch on Konig.
Right on von-der-Tann and Derfflinger, though I believe I still may stand with Moltke and Seydlitz.
The Bayern did have bigger guns but no equivalent Battlecruiser was built so all German capital ships at Jutland, battleship or Battlecruiser had either 11 or 12 inch guns.
True, though the next planned battlecruisers, the Mackensen-class, ordered in 1914, had 35cm guns, vs the Bayern's 38 cm. The next planned "Erstaz Yorck" class battlecruisers would have had 38 cm guns, though the next planned battleship class, "L 20e α"-class was to have 42 cm guns. So, all in all, it seems to me that German battlecruisers of WWI tended to have slightly smaller guns then their contemporary battleship-counterparts? Just to be clear, these would be the guns battleships a class ago used, so still quite formidable I would assume.
The German Battlecruisers had a minimum threat of 12 inch gun so needed battleship grade armour.
The Invincible had a minimum threat of a cruiser gun so had armour sufficient to meet that threat.
The later Lion and Tiger had more armour as the minimum threat was now Von Der Tann and 11 and 12 inch guns. So the German Battlecruisers and the last generation British Battlecruisers were roughly equal in armour and firepower.
von-der-Tann being of course the first German battlecruiser, built 1907-1910. The Lion class was built 1909-1912? I guess the Moltke class would be equivalent, the Lion had 230 mm of belt armor, while the Moltke's had up to 280 mm. Tiger's belt also went to 230 mm, while the Derrflinger's was upped to 300 mm. So it seems to me, that German battlecruisers tended to be better armored than their British counterparts.
Tiger had 13.5 inch guns and 9 inch belt. Hindenburg had 12 inch guns and about 12 inches of armour. The reason for the extra armour was due to Rule Britannia, there was a good chance a German Battlecruiser would run into a British Battleship or due to short numbers, the German Battlecruiser was supposed to fill out the Battle line.
That fits what Drachinifel claimed, that the British BCs were developed to hunt down armoured cruisers doing some commerce raiding and later, after clearing the seas of them, found themselves in the battle-line, while the German BCs were designed for a role in the line from the get-go.
Remember Scharnhorst was designed to have 15 inch guns not 11.
11 was a stop gap and 15 was the goal. One must also look at goals.
You mean classification based on intended role? This is of course a good and reasonable standard of classification. Personally, I have two problems with it:
1: if the navy changes its mind and thus changes the role of the ship, wouldn't that change the class, without a single screw turned on the ship in question?
2: different navies intending different roles for the ships, wouldn't that, too, mean that ships that are virtually identical in their physical characteristics be assigned different classes because their navies had them intended for different roles?
Personally, I would therefor argue to assign classes based on their physical characteristics, especially of course armor, guns and speed.
