We modeled cellular epidermal growth factor receptor (EGFR) tyrosine phosphorylation dynamics in the presence of receptor-targeting kinase inhibitors (e.g., gefitinib) or antibodies (e.g., cetuximab) to identify systematically the factors that contribute most to the ability of the therapeutics to antagonize EGFR phosphorylation, an effect we define here as biochemical efficacy. Our model identifies distinct processes as controlling gefitinib or cetuximab biochemical efficacy, suggests biochemical efficacy is favored in the presence of certain EGFR ligands, and suggests new drug design principles. For example, the model predicts that gefitinib biochemical efficacy is preferentially sensitive to perturbations in the activity of tyrosine phosphatases regulating EGFR, but that cetuximab biochemical efficacy is preferentially sensitive to perturbations in ligand binding. Our results highlight numerous other considerations that determine biochemical efficacy beyond those reflected by equilibrium affinities. By integrating these considerations, our model also predicts minimum therapeutic combination concentrations to maximally reduce receptor phosphorylation.