Human studies of sleep and cognition have established that different sleep stages contribute to distinct aspects of cognitive and emotional processing. However, since the majority of these findings are based on single-night studies, it is difficult to determine whether such effects arise due to individual, between-subject differences in sleep patterns, or from within-subject variations in sleep over time. In the current study, we investigated the longitudinal relationship between sleep patterns and cognitive performance by monitoring both in parallel, daily, for a week. Using two cognitive tasks – one assessing emotional reactivity to facial expressions and the other evaluating learning abilities in a probabilistic categorization task – we found that between-subject differences in the average time spent in particular sleep stages predicted performance in these tasks far more than within-subject daily variations. Specifically, the typical time individuals spent in Rapid-Eye Movement (REM) sleep and Slow-Wave Sleep (SWS) was correlated to their characteristic measures of emotional reactivity, whereas the typical time spent in SWS and non-REM stages 1 and 2 was correlated to their success in category learning. These effects were maintained even when sleep properties were based on baseline measures taken prior to the experimental week. In contrast, within-subject daily variations in sleep patterns only contributed to overnight difference in one particular measure of emotional reactivity. Thus, we conclude that the effects of natural sleep on emotional cognition and category learning are more trait-dependent than state-dependent, and suggest ways to reconcile these results with previous findings in the literature.