Magnetic coupling in ionic solids is studied using a density functional theory, DFT, approach applied to suitable cluster models representing KNiF3, K2NiF4, and La(2)Cuo(4). A mapping between eigenstates of the exact nonrelativistic and spin model Hamiltonians allows us to obtain the magnetic coupling constant J and to compare the DFT values with either experiment or previous theoretical studies based on the use of accurate wave functions. In the present work different correlation and exchange functionals are explored. Numerical results show that it is possible to reach very good agreement with experiment. Surprisingly, it is shown that the difficulty of the local spin density approximation in describing the antiferromagnetic behavior of these compounds lies not in the correlation but in the exchange part of the density functional. Hybrid functionals, which include a component of the full, nonlocal, "exact" exchange interaction yield qualitatively and semiquantitatively correct magnetic interactions. The origin of this behavior is discussed from the point of view of the adiabatic connection formula.