Whether to use LDA or QDA

I'm trying to determine whether it's best to use linear or quadratic discriminant analysis for an analysis that I'm working on. It's my understanding that one of the motivations for using QDA over LDA is that it deals better with circumstances in which the variance of the predictors is not constant across the classes being predicted. This is true for my data, however I intend to carry out principal components analysis beforehand. Because this PCA will involve scaling/normalising the variables, how will this affect the decision to use either QDA or LDA?