To elucidate the distinct effects of relationship conflict (RC) and task conflict (TC), we investigated the intensity (low vs. high) of the two types of conflict on emotional exhaustion and work engagement. Furthermore, we examined how cooperative vs. competitive conflict-handling styles moderate the relationship between the two types of conflict and emotional exhaustion and work engagement. We also examined the role of emotion regulation (cognitive reappraisal and distraction) as a covariate to control its effects on the study variables. Utilizing two separate 2 × 2 between-subject experimental designs, we recruited 120 employees from several companies in Austria. The results suggest that higher levels of both RC and TC are positively related to emotional exhaustion and negatively to work engagement. A cooperative conflict management style moderated the effects of both RC and TC on work engagement. The results suggest decoupling RC and TC and examining the interplay between the intensity of intragroup conflict types and conflict management styles provides insights into the connection between the levels of conflict, conflict management, emotional exhaustion, and work engagement. Additionally, it supports the usage of distraction as a viable regulation strategy for managing the effects of high levels of RC on emotional exhaustion.