A recently developed emulsion-templated assembly method promises the scalable, low-cost, and reproducible fabrication of hierarchical nanocrystal (NC) superstructures. These superstructures derive properties from the unique combination of choices of NC building blocks and superstructure morphology and therefore realize the concept of "artificial solids". To control the final properties of these superstructures, it is essential to control the assembly conditions that yield distinct architectural morphologies. Here, we explore the phase-space of experimental parameters describing the emulsion-templated assembly including temperature, interfacial tension, and NC polydispersity and demonstrate which conditions lead to the growth of the most crystalline NC superstructures or supercrystals. By using a combination of electron microscopy and small-angle X-ray scattering, we show that slower assembly kinetics, softer interfaces, and lower NC polydispersity contribute to the formation of supercrystals with grain sizes up to 600 nm, while reversing these trends yields glassy solids. These results provide a clear path to the realization of higher-quality supercrystals, necessary to many applications.