"How strong is $\Diamond_\kappa^+$?"

Question

In $\text{ZFC}$, we know that $\Diamond_{\kappa}^+ \implies \Diamond_{\kappa}$ and $\Diamond_{\kappa^+} \implies 2^\kappa = \kappa^+$, so that we may think of $\Diamond^+$, i.e. $\Diamond_\kappa^+$ for all infinite cardinals $\kappa$, as a strengthening of $\text{GCH}$. I now wonder how strong $\Diamond^+$ is relative to $\text{GCH}$. In fact, assuming $\text{GCH}$, how much of $\Diamond^+$ can we actually get to fail (, how do we accomplish this) and are there any nice statements, which imply $\text{GCH}$ but not $\Diamond^+$?