Recent works have addressed the automatic cover detection problem from a metric learning perspective. They employ different input representations, aiming to exploit melodic or harmonic characteristics of songs and yield promising performances. In this work, we propose a comparative study of these different representations and show that systems combining melodic and harmonic features drastically outperform those relying on a single input representation. We illustrate how these features complement each other with both quantitative and qualitative analyses. We finally investigate various fusion schemes and propose methods yielding state-of-the-art performances on two publicly-available large datasets.