Piezoelectric composites are a class of smart materials that can be manufactured in a scalable manner through additive processes, while satisfying a wide range of applications. Recent efforts are directed towards lead-free piezoelectric material composites, with the goal of achieving performance comparable to lead-based composites. Although much research has been done in fabrication methodologies such as 3D printing, which allows complex piezoelectric structures to be fabricated in a scalable manner, important questions remain to be addressed to improve the performance of lead-free piezoelectric composites. Fundamental to this is an understanding of the key drivers of piezoelectric performance: electroelastic interactions between the piezoelectric material and the matrix, the effects of the polycrystalline microstructure of piezoelectric inclusions, the effect of randomly shaped polycrystalline fillers, and the effect of the volume fraction of the piezoelectric material in the matrix. We computationally investigate these important aspects of piezoelectric composite design and performance by considering for the first time the polycrystalline nature of lead-free piezoelectric inclusions in the context of a matrix-inclusion composite. Our analysis reveals that although polycrystalline piezoelectric materials, in isolation, can outperform their single-crystalline counterparts, in a composite architecture these improvements are not straightforward. We conclude that these new architectures, devised by combining polycrystalline piezoelectric inclusions in a high permittivity environment, can improve the performance of composites beyond the single-crystal design and thus offer a promising direction for 3D printable lead-free piezoelectric composites.