Thanks to their unique properties, nematic liquid crystals feature a variety of mechanisms for light-matter interactions. For continuous-wave optical excitations, the two dominant contributions stem from reorientational and thermal nonlinearities. We thoroughly analyze the competing roles of these two nonlinear responses with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells and continuous-wave beams at two distinct wavelengths in order to adjust the relative weights of the two responses. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation and compared to experimental results.