Selecting the model is an important and essential step in model based fault detection and diagnosis (FDD). Factors that are considered in evaluating a model include accuracy, training data requirements, calibration effort, generality, and computational requirements. The objective of this study was to evaluate different modeling approaches for their applicability to model based FDD of vapor compression chillers. Three different models were studied: the Gordon and Ng Universal Chiller model (2nd generation) and a modified version of the ASHRAE Primary Toolkit model, which are both based on first principles, and the DOE-2 chiller model, as implemented in CoolToolsTM, which is empirical. The models were compared in terms of their ability to reproduce the observed performance of an older, centrifugal chiller operating in a commercial office building and a newer centrifugal chiller in a laboratory. All three models displayed similar levels of accuracy. Of the first principles models, the Gordon-Ng model has the advantage of being linear in the parameters, which allows more robust parameter estimation methods to be used and facilitates estimation of the uncertainty in the parameter values. The ASHRAE Toolkit Model may have advantages when refrigerant temperature measurements are also available. The DOE-2 model can be expected to have advantages when very limited data are available to calibrate the model, as long as one of the previously identified models in the CoolTools library matches the performance of the chiller in question.