Recently there have been a slew of papers on comparison of different schemes to solve Euler equations, especially in the cosmological context. The most recent work has been http://arxiv.org/abs/0901.4107 and other papers by the same group. They claim that an unstructured (and regularized at every timestep) moving mesh combines the best features of SPH (constant in mass resolution, Galilean invariance) and Eulerian codes (well-resolved and contact discontinuity). Moving mesh has an additional advantage: the contact discontinuity is very sharply resolved because of small diffusion error ($\propto v \Delta x$, where $v$ is the fluid velocity in a non-moving mesh). Therefore a moving mesh mode does very well compared to a fixed-grid method for problems with large advection velocities. The SPH codes aren't even capable of qualitatively simulate turbulence; they don't get the inertial range because of the lack of interaction of equal-sized eddies. The reason is that all eddies except the larges ones are diffused by smoothing noise. So SPH is not good to simulate subsonic flows and there is no easy fix for this.
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