We examine how technological change affects wage inequality and unemployment in a calibrated model of matching frictions in the labor market. We distinguish between two polar cases studied in the literature: a "creative destruction" economy where new machines enter chiefly through new matches and an "upgrading" economy where machines in existing matches are replaced by new machines. Our main results are: (i) these two economies produce very similar quantitative outcomes, and (ii) the total amount of wage inequality generated by frictions is very small. We explain these findings in light of the fact that, in the model calibrated to the U.S. economy, both unemployment and vacancy durations are very short, i.e., the matching frictions are quantitatively minor. Hence, the equilibrium allocations of the model are remarkably close to those of a frictionless version of our economy where firms are indifferent between upgrading and creative destruction, and where every worker is paid the same market-clearing wage. These results are robust to the inclusion of machine-specific or match-specific heterogeneity into the benchmark model.