Recently, our combined diffraction and NMR experiments have shown that alpha-NaMnO2, an antiferromagnet with two-dimensional triangular stacked topology, is a striking example of an insulating system where the spin, degree of freedom induces multiple competing phases. In order to shed light in the role of geometric spin frustration, studies of isostructural compounds by total scattering approaches are highly sought. For this reason we request 5-days of beam time on GEM to raise evidence on the evolution of the near-equivalent structural phases of alpha-NaMnO2 against the case of the isostructural, more homogeneous CuMnO2. By analyzing their atomic pair distribution function (PDF) data, we aim to learn how the competition evolves into locally broken symmetry states when the critical region is approached and the transformation from the disordered to the Néel ordered states takes place.