In view of the extensive use of hexagonal boron nitride (hBN) in 2D material electronics, it becomes important to refine its dielectric characterization in terms of low-field permittivity and high-field strength and conductivity up to the breakdown voltage. The present study aims at filling this gap using DC and RF transport in two Au-hBN-Au capacitor series of variable thickness in the 10-100 nm range, made of large high-pressure, high-temperature (HPHT) crystals and a polymer derivative ceramics (PDC) crystals. We deduce an out-of-plane low field dielectric constant ǫ = 3.4 ± 0.2 consistent with the theoretical prediction of Ohba et al., that narrows down the generally accepted window ǫ = 3-4. The DC-current leakage at high-field is found to obey the Frenkel-Pool law for thermally-activated trap-assisted electron transport with a dynamic dielectric constant ǫ ≃ 3.1 and a trap energy Φ B ≃ 1.3 eV, that is comparable with standard technologically relevant dielectrics.