We present a comprehensive study on the integration of hexagonal boron nitride (h-BN) with epitaxial graphene (EG) and bilayer hydrogen intercalated EG. Charged impurity scattering is the dominant scattering mechanism for as-grown and h-BN coated graphene. Use of h-BN dielectrics leads to a 2.6× improvement in Hall mobility relative to HfO2 by introducing less charged impurities and negligible additional remote surface optical scattering beyond that introduced by the substrate. Temperature dependent mobility measurement is used to link the surface morphology of the silicon carbide substrate (i.e., step-edge density) with charge carrier transport, showing that significant degradation in mobility can result from increased remote charged impurity as well as remote surface optical scattering at the SiC step-edges. Furthermore, we demonstrate that the integration of h-BN with EG and bilayer graphene presents unique challenges compared to previous works on exfoliated graphene, where the benefits of h-BN as a dielectric is highly dependent on the initial quality of the EG. To this end, modeling of the carrier mobility as a function of impurity density is used to identify the regimes where h-BN dielectrics outperform conventional dielectrics and where they fail to surpass them. Modeling indicates that h-BN can ultimately lead to a >5× increase in mobility relative to HfO2 dielectrics due to higher energy surface optical phonon (SOP) modes.