Recently, the field of musical co-creativity has gained some momentum. In this context, our goal is twofold: to develop an intelligent listening and predictive module of chord sequences, and to propose an adapted evaluation of the associated Music Information Retrieval (MIR) tasks that are the real-time extraction of musical chord labels from a live audio stream and the prediction of a possible continuation of the extracted symbolic sequence. Indeed, this application case invites us to raise questions about the evaluation processes and methodology that are currently applied to chord-based MIR models. In this paper, we focus on musical chords since these mid-level features are frequently used to describe harmonic progressions in Western music. In the case of chords, there exists some strong inherent hierarchical and functional relationships. However, most of the research in the field of MIR focuses mainly on the performance of chord-based statistical models, without considering music-based evaluation or learning. Indeed, usual evaluations are based on a binary qualification of the classification outputs (right chord predicted versus wrong chord predicted). Therefore, we present a specifically-tailored chord analyser to measure the performances of chord-based models in terms of functional qualification of the classification outputs (by taking into account the harmonic function of the chords). Then, in order to introduce musical knowledge into the learning process for the automatic chord extraction task, we propose a specific musical distance for comparing predicted and labeled chords. Finally, we conduct investigations into the impact of including high-level metadata in chord sequence prediction learning (such as information on key or downbeat position). We show that a model can obtain better performances in terms of accuracy or perplexity, but output biased results. At the same time, a model with a lower accuracy score can output errors with more musical meaning. Therefore, performing a goal-oriented evaluation allows a better understanding of the results and a more adapted design of MIR models.