Recent evidence suggests that low and high firing neurons display different plasticity and dynamics. We therefore investigated the effects of sleep and waking states and state transitions on hippocampal CA1 neurons with a log-normal distribution of firing rates. We analyzed single unit spiking from 1017 putative pyramidal cells and 116 putative interneurons along with local field potentials of hippocampal CA1 region recorded in 19 sessions from male rats during natural wake/sleep across the 24-hr cycle. We separated cells into five quantiles based on firing rates, and implemented a shuffle-corrected deflection index to account for changes relative to regression to the mean. Firing-rate changes within non-REM sleep, REM sleep, and state transitions from non-REM to REM favored higher-firing neurons, with either smaller increases or stronger decreases among lower-firing neurons. In contrast, transitions from REM to non-REM sleep reduced variability across population, resulting in higher firing among lower-firing neurons and vice versa. These changes account for previously reported net decrease of firing rate across sleep, with the largest decrease occurring in lower-firing cells, while moderately-firing cells show the greatest firing increases during waking. These results demonstrate that sleep/wake states and state transitions affect lower and higher-firing neurons differently, with non-REM sleep playing a normalizing role, and are consistent with competitive interactions that favor higher-firing neurons, and greater plasticity in lower-firing cells.