Both the Stroop and the Simon task are typically viewed as tasks requiring cognitive control: Both tasks include task relevant and task-irrelevant stimulus information, and the main difficulty of the task is to act on the relevant information while ignoring the irrelevant information. Both tasks include a condition in which task relevant and task irrelevant information are compatible, that is, they evoke the same response, and a condition in which the information are incompatible, that is, they evoke different responses. Different theoretical accounts have been proposed, making different assumptions on the nature and location of the conflict. We present the results of an accuracy-based variant of both tasks without time pressure to give a response, minimising the effect of response conflict. The data were modelled with the Theory of Visual Attention (TVA; Bundesen, 1990) framework. The results provide clear evidence for differences between the two tasks in terms of the time relevant and irrelevant stimulus information are available and thus can create conflict. Also, we obtained evidence for the conclusion that a Simon effect is present also in a purely accuracy-based task. We discuss potential implications of these results for cognitive control theories of those tasks and outline a TVA-based model that is applicable to response time data obtained in these tasks.