Both movement and neural activity in humans can be entrained by the regularities of an external stimulus, such as the beat of musical rhythms. Neural entrainment to auditory rhythms supports temporal perception, and is enhanced by selective attention and by hierarchical temporal structure imposed on rhythms. However, it is not known how neural entrainment to rhythms is related to the subjective experience of groove (the desire to move along with music or rhythm), the perception of a regular beat, the perception of complexity, and the experience of pleasure. In two experiments, we used musical rhythms (from Steve Reich’s Clapping Music) to investigate whether rhythms that are performed by humans (with naturally variable timing) and rhythms that are mechanical (with precise timing), elicit differences in (1) neural entrainment, as measured by inter-trial phase coherence, and (2) subjective ratings of the complexity, preference, groove, and beat strength of rhythms. We also combined results from the two experiments to investigate relationships between neural entrainment and subjective perception of musical rhythms. We found that mechanical rhythms elicited a greater degree of neural entrainment than performed rhythms, likely due to the greater temporal precision in the stimulus, and the two types only elicited different ratings for some individual rhythms. Neural entrainment to performed rhythms, but not to mechanical ones, correlated with subjective desire to move and subjective complexity. These data, therefore, suggest multiple interacting influences on neural entrainment to rhythms, from low-level stimulus properties to high-level cognition and perception.