The structural, elastic, anisotropic, and thermodynamic properties of P3m1-BC₇ and Pmm2-BC₇ have been studied in this paper utilizing first-principles calculations. In comparison with the elastic properties of Pmm2-BC₇, P3m1-BC₇ exhibits slightly higher values in bulk modulus and B/G, with similar values in shear modulus, the Young modulus, and the Poisson ratio. The calculated Pugh modulus ratio (B/G) and the Poisson ratio demonstrates P3m1-BC₇ from brittle to ductile at 93.60 and 93.73 GPa, respectively. Calculations of shear anisotropic factor, universal elastic anisotropy index, shear modulus, the Young modulus, and the Poisson ratio for BC₇ then demonstrate that Pmm2-BC₇ exhibits a larger elastic anisotropy than P3m1-BC₇. Quasi-harmonic Debye model is finally applied to investigate the Debye temperature, the coefficient of thermal expansion, heat capacity and Grüneisen parameter of Pmm2-BC₇ and P3m1-BC₇.