We have done differential expression analyses using edgeR and DESeq2. Then we have kept the genes detected by both methods as differentially expressed, trying to be more restrictive or conservative in our findings.
Would it be better to use only the DEGs detected with one method instead of the intersection of both?
There's no guarantee that the false discovery rate is controlled in the intersection (unless you're using intersection-union tests to combine p-values, but I doubt this is what you have done). For example, edgeR will control the error rate across its set of DE genes at a given significance threshold, but that may no longer be the case if an arbitrary external filter is applied. It is for this very reason that we advise against filtering the DE list based on a log-fold change threshold, and to use methods like TREAT instead.
If you want to be more conservative, stick with one method and reduce the FDR threshold. This is a more rigorous approach that ensures the error rate is properly controlled in the DE list. Taking the intersection can also be problematic if power differs between methods. One can imagine an extreme case where two methods are 100% correct (i.e., have no false positives) but yield completely different sets of genes due to differences in power. Using either method in isolation would be more productive than taking the empty intersection.
