Two shock-capturing schemes were considered: characteristic-based MUSCL (monotone upstream-centred schemes for conservation laws) scheme and WENO (weighted essentially non-oscillatory) scheme. Local linearization was employed when performing characteristic transformation, and limiters were applied according to the characteristics of waves; A dimension by dimension reconstruction was used to obtain truly accurate finite volume WENO scheme. Numerical experiments were carried out on one-, two- and three-dimensional Euler systems. The results show with one- and two-dimensional examples that characteristic-based MUSCL scheme performs better on capturing contact discontinuities, and shows little difference from WENO scheme on shocks. For three-dimensional problems, a finer resolution of complex flow feature can be obtained by WENO scheme. Explanations as well as possible improvements are given.