The performance of high-order finite-volume advection upwind schemes based on the second-order tracer reconstruction or gradient reconstruction is compared to the performance of finite-element Taylor-Galerkin (TG) scheme with consistent mass matrix and to the third-order direct time space scheme on regular quadrilateral mesh. The impact of mesh geometry and non-uniformity is briefly analyzed. Although on quasi-equilateral triangular meshes errors of finite-volume schemes prove to be close to those on quadrilateral meshes, the accuracy of simple TG scheme with consistent mass matrix remains in many cases better for smooth perturbations. In practice, however, the TG scheme requires some (for example, FCT) limiting while the upwind finite-volume schemes demonstrate stable performance on their own. The vertex-based placement of scalar quantities on triangular meshes is analogous to the cell-based placement on hexagonal meshes. The schemes analyzed here have very close equivalents on hexagonal meshes which are in focus of atmospheric community.