A finite-volume (FV) discretization method for the lattice Boltzmann (LB) equation, which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. For this reason the comparative analysis is further extended to the case of realistic flows, in particular thermally driven flows in turbulent conditions. We report the successful simulation of high-Rayleigh number convective flow performed by a lattice Boltzmann FV-based algorithm with wall grid refinement.