I ran OLS regression in Stata. Based only on the results I got in OLS, is there any way to know if the quantile regression will be a better choice?
Two cases where quantile regression may be preferred to OLS are when you have outliers and heteroskedastic data. I know it's not a result in the numerical printout for OLS, but you just look at some residual plots and leverage plots.
What's better? Lower MSE? OLS will almost certainly (guaranteed?) be better according to this metric.
In other cases, you would want to define better as "more correctly models the effect of interest." In that case, quantile regression could be better by allowing you to see trends in the bulk of the data.