In DESeq they write:
How do I use the variance stabilized or rlog transformed data for differential testing?
The variance stabilizing and rlog transformations are provided for applications other than differential testing, for example clustering of samples or other machine learning applications. For differential testing we recommend the DESeq function applied to raw counts as outlined in Section 1.4.
Variance grows with mean in rna-seq. With the variance stabilization variance does not depend on mean anymore. But how does it influence differential testing?