Suppose that the stationary series $r_t$ is well fitted by an $ARMA(p,q)+c$ and $GARCH(r,s)$ model, where $GARCH(r,s) = \sigma_t ^2$
If in the testing sample I have to graphically compare the estimated $GARCH (r,s)$ with the actual conditional variance series in order to better visualize the goodness of fit, is it more useful (and maybe correct) directly comparing the $GARCH(r,s)$ series with the $r^2$ series (as actual conditional variance approximation), or the $\sigma_t = \sqrt{\sigma_t^2} = \sqrt{GARCH(r,s)}$ series with the absolute values of $r_t$ ? Or is it equal?