Dealing with strong shocks while retaining numerical dissipation of reasonably low level has been one of the major challenges for high order methods like discontinuous Galerkin. In the literature, various shock capturing models have been designed based on approaches of great distinction. Therefore, it would be insightful to conduct evaluation of different models under the same context. The motivation of the present work is to compare several typical shock capturing models in terms of accuracy and robustness. The selected models consist of a simplified artificial bulk model, a highest model decay model, a averaged model decay model, an entropy viscosity model and a WENO limiting method. Performance for both smooth and non-smooth problems are examined with typical one- and two dimensional cases. The results indicate that for lower accuracy orders(typicall lower than P4), WENO is able to achieve less dissipative results than its viscosity counterparts, while the viscosity models works better for high orders. The simplified artificial bulk model is able to resolve shocks with high accuracy but is limited to second order accuracy around smooth regions. The highest model suers from the inaccurate estimation of the model decay rate, and may give unusually dissipative results for certain orders. The averaged model works well in terms of both accuracy and robustness, with certain oscillations within the element level. The entropy viscosity model is observed to emphasize contact discontinuities more than the other viscosity models.