To localize low-frequency sounds, humans rely on an interaural comparison of the temporally encoded sound waveform after peripheral filtering. This process can be compared with cross-correlation. For a broadband stimulus, after filtering, the correlation function has a damped oscillatory shape where the periodicity reflects the filter's center frequency and the damping reflects the bandwidth (BW). The physiological equivalent of the correlation function is the noise delay (ND) function, which is obtained from binaural cells by measuring response rate to broadband noise with varying interaural time delays (ITDs). For monaural neurons, delay functions are obtained by counting coincidences for varying delays across spike trains obtained to the same stimulus. Previously, we showed that BWs in monaural and binaural neurons were similar. However, earlier work showed that the damping of delay functions differs significantly between these two populations. Here, we address this paradox by looking at the role of sensitivity to changes in interaural correlation. We measured delay and correlation functions in the cat inferior colliculus (IC) and auditory nerve (AN). We find that, at a population level, AN and IC neurons with similar characteristic frequencies (CF) and BWs can have different responses to changes in correlation. Notably, binaural neurons often show compression, which is not found in the AN and which makes the shape of delay functions more invariant with CF at the level of the IC than at the AN. We conclude that binaural sensitivity is more dependent on correlation sensitivity than has hitherto been appreciated and that the mechanisms underlying correlation sensitivity should be addressed in future studies.