Ammonia-oxidizing archaea (AOA) are major players in the nitrogen cycle but their cultivation represents a major challenge due to their slow growth rate and limited tendency to form biofilms. In this study, AOA was embedded in small (~2.5 mm) and large (~4.7 mm) poly(vinyl alcohol) (PVA)—sodium alginate (SA) hydrogel beads cross-linked with four agents (calcium, barium, light, or sulfate) to compare the differences in activity, the diffusivity of nitrogen species (NH4+, NO2−, and NO3−), and polymer leakage in batch systems over time. Sulfate-bound PVA-SA beads were the most stable, releasing the lowest amount of polymer without shrinking. Diffusion coefficients were found to be 2 to 3 times higher in hydrogels than in granules, with ammonium diffusivity being ca. 35% greater than nitrite and nitrate. Despite a longer lag phase in small beads, embedded AOA sustained a high per volume rate of ammonia oxidation compatible with applications in research and wastewater treatment.