We present a comparative study of the low-dimensional compounds alpha- and beta-TeVO4. Our data clearly show that the change in the local coordination geometry of V4+ ions between alpha- and beta-TeVO4 leads to drastic differences in their magnetic properties. Despite sharing the same crystal structure, the two compounds manifest different magnetic exchange topologies. Both compounds exhibit a transition from ferro-to anti-ferromagnetic correlations with decreasing temperature. This effect, however, is driven by different mechanisms in the two compounds. In addition, dimensional crossover is found in beta-TeVO4. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4734010]