Silicon carbide ceramics under shock loading is an important aspect in studying their physical and mechanical properties. Molecular dynamics simulations have been carried out using Tersoff-1989, Tersoff-1994, Tersoff-2005 and Vashishta potentials, respectively. The Hugoniot states including compression stress, shear stress, temperature and shock wave velocity are calculated, as well as shock-induced plasticity and the shock wave fronts. A comprehensive comparison among different potentials, as well as comparison to current available experiments, has been made. Tersoff-1989, Tersoff-1994 and Tersoff-2005 potentials are easily to overestimate the shock stress, shear stress and temperature, as well as shock wave velocity, while Vashishta potential shows excellent agreement with experimental data. The Hugoniot elastic limit is ~ 14.5 GPa and the maximum shear stress is ~ 6 GPa using Vashishta potential which are in good agreement with experiments, while Tersoff-like potentials yield much higher values. Due to differences in radial distribution function among these potentials, Vashishta potential is prone to produce plasticity and structural phase transformation basing on the statistics of the coordination numbers of atoms. Besides, the shock wave fronts show little difference among these potentials under elastic shock compression at low particle velocity. However, when it comes to high shock intensity resulting in plasticity or phase transition, the Tersoff-1989 and Tersoff-1994 produce the widest shock wave fronts, followed by Tersoff-2005, while Vashishta potential has the narrowest wave front. By comprehensive comparisons, the Vashishta potential is demonstrated to be the most suitable one to describe the silicon carbides ceramics under shock loadings. Our work provides useful information to select a suitable potential to study the shock response of silicon carbides ceramics using molecular dynamics simulations.