Neural tracking (entrainment) of auditory rhythms enhances perception. We previously demonstrated that transcranial alternating current stimulation (tACS) can enhance or suppress entrainment to rhythmic auditory stimuli, depending on the timing between the electrical and auditory signals, although tACS effects are primarily modulatory. This study further investigated entrainment to tACS and auditory rhythms when the electrical and auditory signals were presented together (Experiment 1, N = 34) or independently (Experiment 2, N = 24; Experiment 3, N = 12). We hypothesized that tACS effects would be more pronounced when the auditory rhythm was made less perceptually salient to reduce the competition with the electrical rhythm. Participants detected silent gaps in modulated or unmodulated noise stimuli. In Experiment 1, auditory stimuli predominated in entraining behavior. While behavioral entrainment to sound rhythms was affected by the modulation depth of the auditory stimulus, entrainment to tACS was not. In Experiment 2, with no rhythmic information from the sound, 17 of 24 participants showed significant behavioral entrainment to tACS, although the most effective tACS frequency varied across participants. An oscillator model with a free parameter for the individual resonance frequency produced profiles similar to those we observed behaviorally. In Experiment 3, both neural and behavioral entrainment to rhythmic sounds were affected by the auditory stimulus frequency, but again the most effective entraining frequency varied across participants. Our findings suggest that tACS effects depend on the individual's preferred frequency when there is no competition with sensory stimuli, emphasizing the importance of targeting individual frequencies in tACS experiments. When both sensory and electrical stimuli are rhythmic and compete, sensory stimuli prevail, indicating the superiority of sensory stimulation in modulating behavior.