Understanding the nature and extent of sensorimotor decline in aging individuals and those with neurocognitive disorders (NCD), such as Alzheimer's disease, is essential for designing effective music-based interventions. Our understanding of rhythmic functions remains incomplete, particularly in how aging and NCD affect sensorimotor synchronization and adaptation to tempo changes. This study aimed to investigate how aging and NCD severity impact tapping to metronomes and music, with and without tempo changes. Patients from a memory clinic participated in a tapping task, synchronizing with metronomic and musical sequences, some of which contained sudden tempo changes. After exclusions, 51 patients were included in the final analysis. Participants' Mini-Mental State Examination scores were associated with tapping consistency. Additionally, age negatively influenced consistency when synchronizing with a musical beat, whereas consistency remained stable across age when tapping with a metronome. The results indicate that the initial decline of attention and working memory with age may impact perception and synchronization to a musical beat, whereas progressive NCD-related cognitive decline results in more widespread sensorimotor decline, affecting tapping irrespective of audio type. These findings underline the importance of customizing rhythm-based interventions to the needs of older adults and individuals with NCD, taking into consideration their cognitive as well as their rhythmic aptitudes.