Field Emission properties of aligned bundles of SWCNTs decorated by nanodiamond grains have been experimentally studied. Additional information, required to give a physical interpretation to the experimental data, have been acquired by comparing the FE properties of such hybrid materials with those of two types of Single-Walled Carbon Nanotube (SWCNT) samples, constituted by bundles aligned and not aligned along the cathode-anode direction, respectively. For all samples, the characteristics of Field Emission have been described in the frame of the Fowler-Nordheim relationship and analysed following different models. The obtained values of current density from samples formed by SWCNT ensembles suggest that the observations are best accounted by a model based on the mechanism involving field concentration near a nanotube (that is the model generally accepted for SWCNTs and using the β factor). Conversely, if nanodiamond grains decorate the SWCNT bundles, one has to invoke a more complex two-factor model, where the β factor is coupled to another emission mechanism. Two versions of emission model are here considered: (1) the model coupling the β factor to the thermoelectric effect and; (2) the model coupling the β factor to a pre-breakdown process.