The mustached bat (Pteronotus parnellii) is a mammalian model of cortical hemispheric asymmetry. In this species, complex social vocalizations are processed preferentially in the left Doppler-shifted constant frequency (DSCF) subregion of primary auditory cortex. Like hemispheric specializations for speech and music, this bat brain asymmetry differs between sexes (i.e., males>females) and is linked to spectrotemporal processing based on selectivities to frequency modulations (FMs) with rapid rates (>0.5 kHz/ms). Analyzing responses to the long-duration (>10 ms), slow-rate (<0.5 kHz/ms) FMs to which most DSCF neurons respond may reveal additional neural substrates underlying this asymmetry. Here, we bilaterally recorded responses from 176 DSCF neurons in male and female bats that were elicited by upward and downward FMs fixed at 0.04 kHz/ms and presented at 0-90 dB SPL. In females, we found inter-hemispheric latency differences consistent with applying different temporal windows to precisely integrate spectrotemporal information. In males, we found a substrate for asymmetry less related to spectrotemporal processing than to acoustic energy (i.e., amplitude). These results suggest that in the DSCF area, (1) hemispheric differences in spectrotemporal processing manifest differently between sexes, and (2) cortical asymmetry for social communication is driven by spectrotemporal processing differences and neural selectivities for amplitude.