Competence-oriented teaching that leads to the sustainable transformation of both the individual and society requires a holistic learning process that addresses the cognitive, socio-emotional and behavioural domains of learning in a balanced way. This article questions whether a personal dimension of competences (addressing the individual’s values, attitudes, and lived experiences) is relevant for higher education in addition to the systemic dimension (learning objectives emphasizing cognitive processes). A theoretical concept for analysing competence frameworks from this point of view was developed in a multi-step qualitative research process: two existing competence frameworks underpinning international ESD policies were compared and, based on the findings, an analytical tool to analyse competence dimensions was drafted as a two-dimensional matrix. This tool was tested on competence frameworks reported in the literature and on examples from practice in confrontation with related academic discussion. The analysis of sustainability competences with this tool illustrates the transformative dimension on a scale from holistic thinking through future orientation to achieving transformation, and the normative dimension that indicates the complementarity of the personal and systemic character of competences. The analysed competence frameworks include competences more or less evenly distributed in both dimensions; the competences in the socio-emotional learning domain were often associated with envisioning change and achieving sustainable transformation. As anticipating the future in an active way is relevant for sustainability-oriented HE programs, not only should this dimension of competences be afforded greater consideration, but pedagogies addressing the personal level should also be further investigated and implemented in HE.