The electronic and optical properties of zigzag and armchair beta-graphyne nanotubes (beta-GNTs) and their BN analogues (labeled as beta-BNyne NTs) with different tube diameters are systematically investigated by the first-principles calculations. The calculated results reveal that all zigzag and armchair beta-graphyne nanotubes are direct band gap semiconductors. As for zigzag beta-BNyne NTs, they are wide direct band gap semiconductors. Nevertheless, armchair beta-BNyne NTs are indirect band gap semiconductor. The optical spectra of beta-GNTs and BNyne NTs show remarkable anisotropic behavior. Interestingly, the static dielectric constant of beta-GNTs is quite high in comparison with carbon NTs, indicating higher conductivity and carrier mobility. In addition, quite broad frequency absorption spectra, extended from the infrared to the ultraviolet (UV) region, are observed for all beta-GNTs. However, the photoresponse of beta-BNyne NTs is mainly located in the UV region. The beta-GNTs exhibit high reflectivity in the infrared region of 0.0 to 1.5 eV for both parallel and perpendicular polarization, but all beta-BNyne NTs possess very low reflectivity and are highly sensitive to the UV light. Particularly, all beta-GNTs demonstrate no obvious size-dependent optical properties, however, for beta-BNyne NTs, all the photoresponse intensity (static dielectric constant, reflectivity and absorption coefficient) decreases monotonically with increasing tube size.