For listeners with bilateral cochlear implants (BiCIs), patient-specific differences in the interface between cochlear implant (CI) electrodes and the auditory nerve can lead to degraded temporal envelope information, compromising the ability to distinguish between targets of interest and background noise. It is unclear how comparisons of degraded temporal envelope information across spectral channels (i.e., electrodes) affect the ability to detect differences in the temporal envelope, specifically amplitude modulation (AM) rate. In this study, two pulse trains were presented simultaneously via pairs of electrodes in different places of stimulation, within and/or across ears, with identical or differing AM rates. Results from 11 adults with BiCIs indicated that sensitivity to differences in AM rate was greatest when stimuli were paired between different places of stimulation in the same ear. Sensitivity from pairs of electrodes was predicted by the poorer electrode in the pair or the difference in fidelity between both electrodes in the pair. These findings suggest that electrodes yielding poorer temporal fidelity act as a bottleneck to comparisons of temporal information across frequency and ears, limiting access to the cues used to segregate sounds, which has important implications for device programming and optimizing patient outcomes with CIs.