I have a dataset with 10000 data points and 20 features. The features are not normally distributed (most of them have a generalized extreme value or burr distribution and all values are greater or equal to zero). Of course some classifiers requires standardized/normalized features so that the features have similar scale. Because I have some outliers in my data, I think I have to do standardization (and not normalization). Currently I'm subtracting the mean of each feature and dividing by the standard deviation. Another option would be to subtract the median and divide by the IQR.
Which of this two options is better or does it not matter?