Previous studies suggested that people have stable conflict management styles which relate to their personality traits. However, recent research indicates that conflict management requires flexibility to switch between strategies and that this flexibility may relate to cognitive abilities. The interplay between stable preferences and a flexible performance in conflict management is a novel research avenue. We analyzed data from four studies (N = 1104) using a situational judgment test on emotional intelligence that presents conflict situations in the workplace. We tested whether preferences (selecting one's typical behavior) mainly relate to personality traits and performance (selecting the ideal behavior) to cognitive abilities. We found that preferences akin to conflict management styles emerged between individuals; however, these preferences did not reflect tangible differences in personality traits. Considering performance, cognitive abilities were consistently conducive to solving conflicts, while the contribution of personality traits varied across situations, with the possibility that some traits may even hinder conflict resolution in some situations. We provide preliminary evidence on the contributions of both traits and abilities to conflict management, arguing that conflict management research needs to adopt a holistic view that combines both a person's traits and abilities to explain their conflict behavior.