Amongst the various implementations of arterial spin labeling MRI methods for quantifying cerebral perfusion, the QUASAR method is unique. By using a combination of labeling with and without flow suppression gradients, the QUASAR method offers the separation of macrovascular and tissue signals. This permits local arterial input functions to be defined and “model-free” analysis, using numerical deconvolution, to be used. However, it remains unclear whether arterial spin labeling data are best treated using model-free or model-based analysis. This work provides a critical comparison of these two approaches for QUASAR arterial spin labeling in the healthy brain. An existing two-component (arterial and tissue) model was extended to the mixed flow suppression scheme of QUASAR to provide an optimal model-based analysis. The model-based analysis was extended to incorporate dispersion of the labeled bolus, generally regarded as the major source of discrepancy between the two analysis approaches. Model-free and model-based analyses were compared for perfusion quantification including absolute measurements, uncertainty estimation, and spatial variation in cerebral blood flow estimates. Major sources of discrepancies between model-free and model-based analysis were attributed to the effects of dispersion and the degree to which the two methods can separate macrovascular and tissue signal. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.