We present new results from a direct numerical simulation of a three-dimensional homogeneous Rayleigh-Bénard system (HRB), i.e. a convective cell with an imposed linear mean temperature profile along the vertical direction. We measure the SO(3)-decomposition of both velocity structure functions and buoyancy terms. We give a dimensional prediction for the values of the anisotropic scaling exponents in this Rayleigh-Bénard systems. Measured scaling does not follow dimensional estimate, while a better agreement can be found with the anisotropic scaling of a different system, the random-Kolmogorov-flow (RKF) (Biferale L., Daumont I., Lanotte A. and Toschi F. Phys. Rev. E, 66 (2002) 056306). Our findings support the conclusion that scaling properties of anisotropic fluctuations are universal, i.e. independent of the forcing mechanism sustaining the turbulent flow.