In the field of cognitive control (the ability to direct and control our cognitive function as we intend), the conflict adaptation account has emerged as a foundational construct explaining how control is recruited. Namely, how it is enlisted in response to and with the purpose of overcoming conflict between cognitive processing pathways, ultimately focusing on that which we intend to focus on. In recent years, this theory has been contested by a separate account of control, namely the Parallel Episodic Processing (PEP) model that seeks to demonstrate that much of the evidence illustrating cognitive control can alternatively, and perhaps more appropriately, be explained by more simple learning and memory-based mechanisms independent of conflict monitoring. While the PEP model has been used in many tries to target specific elements of conflict monitoring, this paper seems to be the first attempt in the literature to compare the underlying neural-network computation models of the two potential explanations side by side under similar conditions. More specifically, we are analyzing how the two models differ, and perhaps are similar, in how they work through several control-related well-studied cognitive effects such as Proportion Congruency in the Stroop task and Item Specific Proportion Congruency , and what we can learn about their theoretical assumptions and their effectiveness as a result.