Well, there were several reasons why British battlecruisers fared badly. Armor is one reason, with German battlecruisers having significantly more armor, and better sub-compartmentisation of the ship too. Second, the propellant charges for the German shells were in brass or tin cartridges, while the British cordite charges were lying around in flammable silk bags all along the ammunition train from the magazine to the guns, and third, the British battlecruisers had no passage flaps between the shell ready rooms at the base of the barbette and the ammunition stores, which meant any flash from a shell bursting in the turret overhead would travel right down the barbette and straight into the ammunition magazine..... But these issues were not really noticed by the British until Jutland (when of course, it was too late). At the Falklands, the two British battlecruisers (armed with 8 x 12" guns each) were facing two German armored cruisers (only equipped with 8" guns), and thus were able to stay well out of range of most of the the German guns while pounding the crap out of the Germans with impunity in precisely the kind of action battlecruisers were actually designed to do.
At Dogger Bank, the German armored cruiser 'Blucher' went down, for the same reason as the 'Sharnhorst' and her sister at the Falklands; they were just not up to the task of taking on a battlecruiser, nor were they designed to. As well, the British screwed up pretty badly in this exercise, by directing most of the gunfire of their battlecruisers against the hapless 'Blucher,' while allowing the outnumbered German battlecruisers to escape. Several of these ships had been hit by heavy British rounds, and one was almost lost by the kind of explosion that devastated the British battlecruisers at Jutland. The Germans learned from this almost-catastrophe, and altered their ammunition handling methods accordingly, while the British did not.
In WW2, the incident of the Renown and the 'Salmon & Gluckstein' was one of the worst efforts by the Kriegsmarine, in that they wasted almost 20 minutes trying to figure out whether the very large warship rapidly approaching them was friend or foe (just how many large friendly warships they might reasonably expect to see in the North Sea at that time is a question no-one has ever been able to answer for me!). In any case, rather than forming a line of battle and turning broadside to paste the approaching Renown by 'crossing the T,' they turned and ran as soon as Renown opened up with her 15" guns. What should have been a battle of 18 x 11" guns against 4 x 15" guns turned into a ridiculous Monty Python 'run away' scenario, and the only reason Renown didn't catch up to the Germans and really do them some damage is the Renown was shipping so much water over her bows that the forward turrets became almost useless and the ship was sure to suffer structural damage (not just 'oilcanning!') if the pursuit continued at the speed the Germans were fleeing (at over 28 knots straight into the teeth of a strong gale). An extremely poor show by the Germans, and Hitler was none too pleased when he heard the details!