Universities are increasingly evaluated on the basis of their outputs. These are often converted to simple and contested rankings with substantial implications for recruitment, income, and perceived prestige. Such evaluation usually relies on a single data source to define the set of outputs for a university. However, few studies have explored differences across data sources and their implications for metrics and rankings at the institutional scale. We address this gap by performing detailed bibliographic comparisons between Web of Science (WoS), Scopus, and Microsoft Academic (MSA) at the institutional level and supplement this with a manual analysis of 15 universities. We further construct two simple rankings based on citation count and open access status. Our results show that there are significant differences across databases. These differences contribute to drastic changes in rank positions of universities, which are most prevalent for non-English-speaking universities and those outside the top positions in international university rankings. Overall, MSA has greater coverage than Scopus and WoS, but with less complete affiliation metadata. We suggest that robust evaluation measures need to consider the effect of choice of data sources and recommend an approach where data from multiple sources is integrated to provide a more robust data set.