We explore on the basis of a simple survey tool the "perceived" impact of the Erasmus mobility experience on the improvement of the thirty generic competences of the Tuning Europe list. We rely on a self-assessment procedure, i.e. on data collected by the Erasmus Office of the University of Padova, Italy, through end-of-stay questionnaires, as returned by both outgoing and incoming Erasmus students. Processed data yield the percentage number of ticks, by which a given competence was chosen by the answering samples. We introduce a quantity "importance of improvement", which measures the perceived degree of development of a given generic competence during the mobility experience and allows a consistent comparison among different samples. On this basis, we can order the thirty competences according to decreasing perceived importance of improvement in the two above samples. From a general point of view, Erasmus students perceive the most important improvement in instrumental competences. We can then carry out meaningful comparisons between the profiles of competences' improvement of outgoing and incoming students, both in qualitative and in quantitative terms. Such a comparison reveals interesting features linked to the academic and human environments of mobile students. A further step in the analysis describes how country effects give more insight into the previous results. In such a context, we analyze the country impact on each given competence for both outgoing (visiting the country) and incoming (from the country) students, on the country subgroup competences' profile and on the exchange of competences, which occurs between paired country subgroups.