Bilateral cochlear implants (BICIs) provide improved sound localization and speech understanding in noise compared to unilateral CIs. However, normal-hearing (NH) listeners demonstrate superior binaural processing abilities compared to BICI listeners. This investigation sought to understand differences between NH and BICI listeners' processing of interaural time differences (ITDs) and interaural level differences (ILDs) as a function of fine-structure and envelope rate using an intracranial lateralization task. The NH listeners were presented band-limited acoustical pulse trains and sinusoidally amplitude-modulated tones using headphones, and the BICI listeners were presented single-electrode electrical pulse trains using direct stimulation. Lateralization range increased as fine-structure rate increased for ILDs in BICI listeners. Lateralization range decreased for rates above 100 Hz for fine-structure ITDs, but decreased for rates lower or higher than 100 Hz for envelope ITDs in both groups. Lateralization ranges for ITDs were smaller for BICI listeners on average. After controlling for age, older listeners showed smaller lateralization ranges and BICI listeners had a more rapid decline for ITD sensitivity at 300 pulses per second. This work suggests that age confounds comparisons between NH and BICI listeners in temporal processing tasks and that some NH-BICI binaural processing differences persist even when age differences are adequately addressed.