We use gas-dynamical simulations of galaxy clusters to compare their X-ray and strong lensing properties. Special emphasis is laid on mass estimates. The cluster masses range between 6 x 10(14) and 4 x 10(15) M(.), and they are examined at redshifts between 1 and 0. We compute the X-ray emission of the intracluster gas by thermal bremsstrahlung, add background contamination, and mimic imaging and spectral observations with current X-ray telescopes. Although the beta model routinely provides excellent fits to the X-ray emission profiles, the derived masses are typically biased low because of the restricted range of radii within which the fit can be done. For beta values of similar to 2/3, which is the average in our numerically simulated sample, the mass is typically underestimated by similar to 40 per cent. The masses of clusters that exhibit pronounced substructure are often substantially underestimated. We suggest that the ratio between peak temperature and emission-weighted average cluster temperature may provide a good indicator for ongoing merging and, therefore, for unreliable mass estimates. X-ray mass estimates are substantially improved if we fit a King density profile rather than the beta model to the X-ray emission, thereby dropping the degree of freedom associated with beta. Clusters selected for their strong lensing properties are typically dynamically more active than typical clusters. Bulk flows in the intracluster gas contain a larger than average fraction of the internal energy of the gas in such objects, hence the measured gas temperatures are biased low. The bulk of the optical depth for are formation is contributed by clusters with intermediate rather than high X-ray luminosity. Arcs occur predominantly in clusters that exhibit substructure and are not in an equilibrium state. Finally, we explain why the X-ray emission of some observed are clusters is cooler than predicted from the are geometry. All clusters for which this happens in our simulations show structure in velocity space, indicating ongoing merging along the line of sight. The temperature discrepancy is probably a projection effect.
