It is often asserted that DHE detects superoxide, while DCFH-DA detects hydrogen peroxide (in the presence of peroxidases), hydroxyl radical and peroxynitrite. However, situation is more complex due to numerous interferences ( e.g. H2O2 can oxidize DHE in the presence of myeloperoxidase, cytochrome c can oxidize both DHE and DCFH-DA), so it is better to consider these probes to be markers of cellular oxidative stress rather than indicators of specific ROS or RNS species.
The choice depends on your specific research aims. I suggest that you read this helpful article and make your selection based on a biological question that you want to answer.
Gomes A, Fernandes E, Lima JL. Fluorescence probes used for detection of reactive oxygen species. J Biochem Biophys Methods. 2005 Dec 31;65(2-3):45-80. PubMed PMID: 16297980.