There exist different phase-field models for the simulation of grain growth in polycrystalline structures. In this paper, the model formulation, application and simulation results are compared for two of these approaches. First, we derive relations between the parameters in both models that represent the same set of grain boundary energies and mobilities. Then, simulation results obtained with both models, using equivalent model parameters, are compared for grain structures in 2D and 3D. The evolution of the individual grains, grain boundaries and triple junction angles is followed in detail. Moreover, the simulation results obtained with both approaches are compared using analytical theories and previous simulation results as benchmarks. We find that both models give essentially the same results, except for differences in the structure near small shrinking grains which are most often locally and temporary for large grain structures. (C) 2009 Elsevier B.V. All rights reserved.