In the search for an educational system that enables students to achieve the best academic results, it is extremely important to explore the perception of the main educational agents: students and teachers. Therefore, the objectives of this paper were: (a) to analyse primary school student and teacher perceptions of students' competency-based learning; (b) to assess the possible differences between them; and (c) to test hypothetical models for predicting learning according to their perception. The participants were 8,513 students from 58 schools and 1,010 teachers from 110 schools. Overall, both teachers and students reported high scores of perception. However, the perception of the students was higher than that of the teachers, except for the digital competence. While the results showed differences in perception between both prediction models of competency-based learning, both groups perceived the competences of autonomy and personal initiative, digital competence, social competence and citizenship, and lifelong learning as core elements of their perception. In this regard, initial and ongoing teacher training in innovative pedagogical models is needed to enable the development of these competences, which are predictors of perceived learning.