For many individuals, music has a significant impact on the quality and enjoyability of life. Cochlear implant (CI) users must cope with the constraints that the CI imposes on music perception. Here, we assessed the musical experiences of young CI users and age-matched controls with normal hearing (NH). CI users and NH peers were divided into subgroups according to age: children and adolescents. Participants were tested on their ability to recognize vocal and instrumental music and instruments. A music questionnaire for pediatric populations (MuQPP) was also used. CI users and NH peers identified a similar percentage of vocal music. CI users were significantly worse at recognizing instruments (p < 0.05) and instrumental music (p < 0.05). CI users scored similarly to NH peers on the MuQPP, except for the musical frequency domain, where CI users in the children subgroup scored higher than their NH peers (p = 0.009). For CI users in the children subgroup, the identification of instrumental music was positively correlated with music importance (p = 0.029). Young CI users have significant deficits in some aspects of music perception (instrumental music and instrument identification) but have similar scores to NH peers in terms of interest in music, frequency of music exposure, and importance of music.