Two well-known response interference tasks are the Eriksen flanker task and the spatial conflict task. The tasks are logically equivalent, and comparable effects of current and previous stimulus type (congruent or incongruent) have been shown with regard to reaction time (RT). Here, we investigated whether interference and sequential trial effects also had comparable effects on accuracy. We specifically tested whether these effects interacted with the speed of responding using conditional accuracy functions (CAFs). The CAFs revealed that in both tasks congruency and sequential trial effects on accuracy are found only in trials with fast responses (< 600 ms). Sequential trial effects on accuracy were weaker for the flanker task than for the spatial conflict task. In very fast trials (< 400 ms) response activation by distracting flankers led to below-chance performance in the flanker task, but response activation by incongruent spatial location did not lead to below-chance performance in the spatial conflict task. The pattern of results hints at subtle differences in processing architecture between the tasks.