The present paper tests a new model comparison methodology by comparing multiple calibrations of three agent-based models of financial markets on the daily returns of 24 stock market indices and exchange rate series. The models chosen for this empirical application are the herding model of Gilli and Winker (2003), its asymmetric version by Alfarano et al. (2005) and the more recent model by Franke and Westerhoff (2011), which all share a common lineage to the herding model introduced by Kirman (1993). In addition, standard ARCH processes are included for each financial series to provide a benchmark for the explanatory power of the models. The methodology provides a consistent and statistically significant ranking of the three models. More importantly, it also reveals that the best performing model, Franke and Westerhoff, is generally not distinguishable from an ARCH-type process, suggesting their explanatory power on the data is similar.