I dont really think they were "better" for a given definition of better. Each had strengths and weaknesses, and a major weakness of the British battlecruisers happened to be who commanded them and his incompetent signals officer. Agree on the second bit though, a few extra rounds here and there really wasnt worth the exchange of turning your shiny new battlecruiser into the worlds most expensive firecracker.German battlecruisers were better designed than their British counterparts. However, those British BCs were lost because of poor safety procedures, not necessarily because they had weak armor protection.
Trying to remember where I read, or heard it, but I recall seeing that at Jutland no shot managed to penetrate more than like six inches of armor. Presumably this was due to a number of factors if true, which I cant recall off the top of my head where exactly every BB and BC took their hits and what the armor thickness at the location was obviously. But if it is true then it shows that the earlier British ships were not as badly protected as some like to claim.
Of course there are probably several factors at play here which might be hard to replicate every time if that snipped of mental clutter is true, such as the relative lack of involvement of the German battleships in the battle, the angle of belt relative to shot trajectory, angle of fire entirely, aim of the firing vessel, and a million other variables.