Universities all around the world operate by following several institutional missions, with a central purpose on teaching and research activities. The importance of each aspect alongside the connection between them provide a disputed topic in the literature, many authors confirming or rejecting the intuitive inverse relationship by using various means, more or less quantitative. This paper aims to examine the teaching and research dimensions of the research-active European universities from a data mining perspective. For each dimension previously considered we employ the K-means Clustering in order to identify the groups of similar higher education institutions and we analyze the insights produced by the results. In addition, we build some target variables considering the teaching and research outputs and we investigate their drivers by employing the Logistic Regression. Furthermore, we explore the controverted relationship between the two institutional missions we considered through the use of Correspondence Analysis. Preliminary results illustrate that the dataset contains two types of universities: a category of very large and prestigious institutions and a second group of small and medium sized institutions, quite different from each other. Interest insights are given by the third part of the study, in which the Correspondence Analysis confirms an inverse relationship between teaching and research activities. Unfortunately, this is very likely a consequence of the time constraint – both activities require the same limited resources and therefore increasing the teaching burden for academics may diminish the time and energy dedicated to research.