Both edgeR and DESeq2 are both well-established methods developed for RNAseq data analysis. They differ in their method of data normalization and the algorithms used for estimation of dispersion.
In general, edgeR is more powerful (detecting more DE features) but also comes with higher false positives. DESeq2 is more robust in estimating the DE features (i.e. low false positive rates). DESeq2 is more computationally intensive and may take a long time for large data sets. For more details about their implementation please refer to DESeq2 and EdgeR papers.