The neural mechanisms underlying the exogenous coding and neural entrainment to rapid auditory stimuli have seen a recent surge of interest. However, few studies have characterized how parametric changes in stimulus presentation alter entrained responses. Applying inter-trial phase-locking (ITPL) and phase-locking value (PLV) analyses applied to high-density human electroencephalogram (EEG) data, we investigated the degree to which the brain entrains to speech vs. non-speech (i.e., click) sounds within and across tokens. Passive cortico-acoustic tracking was investigated in N=24 normal young adults utilizing EEG time-frequency and source analyses that isolated neural activity stemming from both auditory temporal cortices. We parametrically manipulated the rate and periodicity of repetitive, continuous speech and click stimuli to investigate how speed and jitter in ongoing sounds stream affect oscillatory entrainment. Both stimulus domains showed rightward hemisphere asymmetry in phase-locking strength with stronger and earlier responses to speech vs. clicks. Neuronal synchronization to speech was enhanced at 4.5 Hz (the putative universal rate of speech) and showed a differential pattern to that of clicks, particularly at higher rates. Phase-locking to speech decreased with increasing jitter but entrainment to speech remained superior to clicks. Surprisingly, click were invariant to periodicity manipulations. Our findings provide evidence that the brain's neural entrainment to complex sounds is enhanced and more sensitized when processing speech relative to non-speech sounds. That this specialization is apparent even under passive listening suggests a priority of the auditory system for synchronizing to behaviorally-relevant signals.