Ground penetrating radar (GPR) is a well-established geophysical technique, that has been applied for about two decades. In particular GPR is used, via specific relationships, to estimate hydrological parameters in vadose zone, i.e. moisture content, both from the surface and in boreholes. In this work we compare two of the most widely used GPR techniques, Vertical Radar Profile (VRP) and Zero-Offset Profile (ZOP), both on real and synthetic datasets. The estimation of a relative permittivity profile from VRP data is achieved via a method based on the minimum support stabilizer, applied to the VRP travel-time inverse problem. This stabilizer makes it possible to produce more accurate profiles of geological targets having sharp boundaries. The estimation of the permittivity profile from ZOP data is based on a forward Monte Carlo framework that generates the expected travel times by means of full waveform modelling, thus reproducing all physical processes that contribute to profile smoothing: Fresnel volume and critically refracted waves. Results from synthetic and real ZOP datasets are stochastically inverted to yield the likely subsoil permittivity distributions that generate them, and the associated uncertainty range. The proposed approach proves to be capable of reconstructing sharp dielectric profiles, in addition to assigning relevant uncertainty bounds derived from the expected errors in travel time picking and from regions which are not investigated with this cross-hole configuration.