Recent stereo algorithms have achieved impressive results by modelling the disparity image as a Markov Random Field (MRF). An important component of an MRF-based approach is the inference algorithm used to find the most likely setting of each node in the MRF. Algorithms have been proposed which use Graph Cuts or Belief Propagation for inference. These stereo algorithms differ in both the inference algorithm used and the formulation of the MRF. It is unknown whether to attribute the responsibility for differences in performance to the MRF or the inference algorithm. We address this through controlled experiments by comparing the Belief Propagation algorithm and the Graph Cuts algorithm on the same MRF's, which have been created for calculating stereo disparities. We find that the labellings produced by the two algorithms are comparable. The solutions produced by Graph Cuts have a lower energy than those produced with Belief Propagation, but this does not necessarily lead to increased performance relative to the ground-truth.