  Two approaches to the construction of integral models of local
Shimura-varieties are compared: that of B\"ultel-Pappas using
$\mathcal{G}$-$\mu$-displays and that of Scholze using local
mixed-characteristic shtuka. As an application, the representability of the
diamond of the generic fiber of the B\"ultel-Pappas moduli problem is verified
and a local representability conjecture of Rapoport-Pappas is proven. The
methods apply to all unramified local Shimura-data under a certain condition on
slopes and if $p\neq 2;$ thus in particular also to exceptional groups.
