The Boltzmann transport equation is one of the most relevant frameworks to study the heat transport at the nanoscale, beyond the diffusive regime and up to the micrometer-scale. In the general case of 3D devices, the particle Monte Carlo approach of phonon transport is particularly powerful and convenient, and requires reasonable computational resources. In this work, we propose an original and versatile particle Monte Carlo approach parametrized by using ab initio data. Both the phonon dispersion and the phonon-phonon scattering rates have been computed by DFT calculation in the entire 3D Brillouin zone. To treat the phonon transport at rough interfaces, a combination of specular and diffuse reflections has been implemented in phase space. Thermal transport has been investigated in nanowires and thin films made of cubic and hexagonal Silicon, including edge roughness, in terms of effective thermal conductivity, phonon band contributions and heat flux orientation. It is shown that the effective thermal conductivity in quasi-ballistic regime obtained from our Monte Carlo simulation cannot be accurately fitted by simple semi-analytical Matthiessen-like models and that spectral approaches are mandatory to get good results. Our full band approach shows that some phonon branches exhibiting a negative group velocity in some parts of the Brillouin zone may contribute negatively to the total thermal flux. Besides, the thermal flux clearly appears to be oriented along directions of high density of states. The resulting anisotropy of the heat flux is discussed together with the influence of rough interfaces.