Resonant ultrasound spectroscopy was used to determine elastic constants and internal friction parameters of bulk nanoparticle-based ceramic materials compacted by spark plasma sintering. Boron nitride-based and boron carbon nitride-based materials were studied, and the results were compared with similar bulk materials prepared from graphene nanoplatelets. The results showed that such nanoparticle-based materials can be strongly anisotropic, and can have very different elastic constants depending on the nanoparticles used. From the temperature dependence of the internal friction parameters, the activation energy for sliding of the individual monolayers along each other was determined for each material. Very similar values of the activation energy were obtained for boron nitride, boron carbon nitride, and graphene, ranging from 15 to 17 kJ/mol.