In principle, it is best if coordinate system triplications are avoided. However, for velocity models with large contrasts (e.g. salt), avoiding such triplications may require large smoothing prior to ray tracing. In these situations, there is a strong possibility that the waves do not propagate close to the extrapolation axis, thus requiring higher-order terms in the extrapolator at increased cost.
A second consideration is that we are comparing extrapolation in different domains (space for downward continuation and shooting angle for Riemannian extrapolation). Since in Riemannian coordinates we extrapolate at small angles, we can sample the wavefronts less and achieve same or better angular accuracy than in Cartesian coordinates at lower cost.