When speech understanding abilities differ across the ears, auditory attention and listening effort could be impacted. Twenty listeners with bilateral cochlear implants (CIs) completed this experiment. Fourteen listeners had symmetric and six listeners had asymmetric functional hearing. Listeners completed monotic and dichotic digit recall with digit string lengths of four and six digits and attention directed to each ear. Pupil size was monitored as an index of listening effort. Individual differences in working memory and inhibition abilities were measured. It was hypothesized that ear asymmetry would lead to poorer listening performance and higher listening effort, and that cognitive abilities would predict both performance and listening effort. Greater differences in performance across ears were observed with asymmetry. Lower listening effort was observed with asymmetry, regardless of which ear was attended. Poorer working memory abilities predicted higher listening effort. These results suggest that asymmetric listeners may experience reduced perception of a poorer ear, and that individuals with poorer working memory abilities are at risk to experience higher listening effort in complex listening environments with CIs. More broadly, these results suggest that the salience of sensory inputs contributes to auditory attention ability and use of cognitive resources.