Protein phosphorylation underlies cellular response pathways across eukaryotes and is governed by the opposing actions of phosphorylating kinases and de-phosphorylating phosphatases. While kinases and phosphatases have been extensively studied, their organization and the mechanisms by which they balance each other are not well understood. To address these questions we performed quantitative analyses of large-scale 'omics' datasets from yeast, fly, plant, mouse and human. We uncovered an asymmetric balance of a previously-hidden scale: Each organism contained many different kinase genes, and these were balanced by a small set of highly abundant phosphatase proteins. Kinases were much more responsive to perturbations at the gene and protein levels. In addition, kinases had diverse scales of phenotypic impact when manipulated. Phosphatases, in contrast, were stable, highly robust and flatly organized, with rather uniform impact downstream. We validated aspects of this organization experimentally in nematode, and supported additional aspects by theoretic analysis of the dynamics of protein phosphorylation. Our analyses explain the empirical bias in the protein phosphorylation field toward characterization and therapeutic targeting of kinases at the expense of phosphatases. We show quantitatively and broadly that this is not only a historical bias, but stems from wide-ranging differences in their organization and impact. The asymmetric balance between these opposing regulators of protein phosphorylation is also common to opposing regulators of two other post-translational modification systems, suggesting its fundamental value.