We have investigated two original hydrated cobalt arsenates based on Co2+ octahedral edge-sharing chains. Their different magnetocrystalline anisotropies induce different types of metamagnetic transitions: spin-flop versus spin-flip. In both compounds, a strong local anisotropy (Ising spins) is favored by the spin-orbit coupling present in the CoO6 octahedra, while ferromagnetic (FM) exchanges predominate in the chains. Co2(As2O7)·2H2O (1) orders antiferromagnetically below TN = 6.7 K. The magnetic structure is a noncollinear antiferromagnetic spin arrangement along the zigzag chains with DFT calculations implying frustrated chains and weakened anisotropy. A metamagnetic transition suggests a spin-flop process above μ0H = 3.2 T. In contrast, in BaCo2As2O8·2H2O (2) linear chains are arranged in disconnected layers, with only interchain ferromagnetic exchanges, therefore increasing its magnetocrystalline anisotropy. The magnetic structure is collinear with a magnetic easy axis that allows a spin-flop to a sharp spin-flip transition below TN = 15.1 K and above μ0H = 6.2 T.