[en] Some polycrystalline forms of the K- and Co-doped BaFe₂As₂ and SrFe₂As₂ superconductors now have a critical current density (J_c) within a factor of ∼5 of that required for real applications, even though it is known that some grain boundaries (GBs) block current, thus, raising the question of whether this blocking is intrinsic or extrinsically limited by artefacts amenable to improvement by better processing. Herein, we utilize atom-probe tomography (APT) to study the grain and GB composition in high J_c K- and Co-doped BaFe₂As₂ polycrystals. We find that all GBs studied show significant compositional variations on the scale of a few coherence lengths (ξ), as well as strong segregation of oxygen impurities, which we believe are largely introduced in the starting materials. Importantly, these findings demonstrate that APT enables quantitative analysis of the highest J_c K-doped BaFe₂As₂ samples, where analytical transmission electron microscopy (TEM) fails because of the great reactivity of thin TEM samples. The observations of major chemical perturbations at GBs make us cautiously optimistic that there is a large extrinsic component to the GB current blocking, which will be ameliorated by better processing, for which APT will likely be a crucial instrument.