Robust regression is simply going to fit your regression model using OLS and then perform an additional weighted regression to provide your final model. The weighting by default uses the bi-squared weighting algorithm. This is essentially going to remove any observations with very large residuals from the initial OLS model, and bias those which are close to the original solution.
If you really want to simply compare a Quadratic and Linear model, I would suggest looking at the AIC and BIC models as they penalize the number of parameters in the fit. These are located in the ModelCriterion property of the LinearModel.
You could also use a stepwise regression to have MATLAB determine based on the AIC or BIC (Akaike and Bayesian Information Criterion respectively)of the model which is the more appropriate fit.
This will start at a linear model and include up to a quadratic model. It will then return to you the best model according to the BIC.