BaTiO3 appears in cubic and hexagonal variants, both of which are centrosymmetric. Samples of cubic BaTiO3 are known to exhibit breaking of the centric symmetry locally and globally. It has been proposed that the local symmetry breaking originates in polar regions, the precursors of the ferroelectric phase. Origins of the macroscopic symmetry breaking, which are not well understood, have been previously tentatively correlated with inhomogeneities in the samples, such as strain gradients that may align or redistribute objects such as charged point defects or polar regions making material macroscopically polar. No such data are available for BaTiO3 with hexagonal symmetry. We compare dielectric, elastic, and pyroelectric properties of the two materials in polycrystalline form. In contrast to cubic BaTiO3, hexagonal BaTiO3 does not exhibit macroscopic pyroelectric response at room temperature. This is consistent with apparent absence of polar regions in the hexagonal material, and the fact that in hexagonal BaTiO3, strain rather than polarization is the order parameter for the phase transition into ferroelectric-ferroelastic phase. The thermally stimulated currents measured in hexagonal and cubic BaTiO3, however, show that both materials exhibit noncentric macroscopic symmetry. This result supports the idea that extrinsic factors, such as strain gradients, which are apparently common for both materials, may break the macroscopic symmetry, which may then lead to alignment and redistribution of polar regions or charged defects.