If both models fit their closed form formulas to market prices, why should I prefer a more complex model? ($\mathbb{Q}$ version has one extra parameter $\lambda$)
Do valuation with dynamics work better under the $\mathbb{Q}$-measure version?
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2$\begingroup$ Most practitioners don't really look at the market price of risk. So they assume exactly the same form of the Heston model under P as under Q, except in the latter the parameters are calibrated to options prices, and in the former to historical time series of the stock. Hence, no added complication under Q. $\endgroup$– FridoMar 2 at 16:37
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