It is becoming ever more common to use bibliometric indicators to evaluate the performance of research institutions, however there is often a failure to recognize the limits and drawbacks of such indicators. Since performance measurement is aimed at supporting critical decisions by research administrators and policy makers, it is essential to carry out empirical testing of the robustness of the indicators used. In this work we examine the accuracy of the popular "h" and "g" indexes for measuring university research performance by comparing the ranking lists derived from their application to the ranking list from a third indicator that better meets the requirements for robust and reliable assessment of institutional productivity. The test population is all Italian universities in the hard sciences, observed over the period 2001-2005. The analysis quantifies the correlations between the three university rankings (by discipline) and the shifts that occur under changing indicators, to measure the distortion inherent in use of the h and g indexes and their comparative accuracy for assessing institutions.