The main difference between constant-velocity and variable-velocity dip moveout is not much the shape of the operator but the amplitude distribution. Because this distribution highly depends on the velocity model, the variable-velocity dip moveout considerably improves the post-stack migration. However, the drawback is the high computational cost. For example, Artley's method is more costly than a pre-stack migration, because the algorithm does much more than computing the zero-offset traveltime: it performs a ray-based pre-stack migration and uses the computed zero-offset traveltime to apply the dip moveout correction. Because Meinardus or Artley's algorithms are based on the dip-decomposition idea, it is possible to reduce the computational cost by cutting down the number of dips to process.
In order to improve the quality of the processing, one must pay a computational cost. In the majority of the practical cases, constant velocity dip moveout will give the best trade-off between the quality of the processing and the computational efficiency, especially if it runs on parallel machines.