Hydroxide-exchange membrane (HEM) fuel cells are emerging energy conversion technologies. A significant effort has been expended to develop new HEMs with enhanced transport functionality, which has driven the need for understanding how transport of hydroxide and other anions in these membranes is related to hydration and nano-morphology. In this work, we report the results of a systematic study on poly(aryl piperidinium)-based on terphenyl (PAP-TP-85), a HEM that previously showed promising fuel cell performance and durability. Membrane water uptake and anion conductivity in liquid and vapor water, as well as the impact of counter-anion forms on these properties, are investigated and compared with a commercial anion exchange membrane (AEM), Fumasep FAA3, and proton-exchange membranes (PEMs), Nafion and sPEEK. Different water uptake in liquid vs. saturated vapor is observed for both AEMs (i.e., PAP and FAA3), indicating Schroeder's paradox, regardless of anion form. Morphology of AEMs examined via small-angle X-ray scattering (SAXS) shows weak phase-separation, regardless of hydration level and anion type, which is attributed to the reduced chemical dissimilarity between the backbone and ionic moieties. Despite both AEMs' amorphous nanostructure, PAP-AEM has a higher ion conductivity than FAA3. Water content plays a more significant role than does temperature in controlling the anion conductivity in water vapor. In liquid water, normalized conductivity shows a universal dependence on hydration, regardless of the anion form. Moreover, in water vapor, conductivity is influenced more by ion mobility than ion concentration, and depends mainly on hydration. Thus, ion transport in disordered AEMs is governed primarily by hydration, in contrast to phase-separated ionomers, where ion transport is governed by nanostructure-hydration interplay. This study demonstrates the importance of hydration level and ion mobility for anion transport in amorphous AEMs and provides an understanding of parameters governing their transport properties.