ForHandledFiles is where the files go after Data Importer has read them and sent them to DataPage. These files
could be deleted, if you
really want to, but I would suggest that you archive them all somewhere. In a worst case scenario, you could completely rebuild the database from these files if the database were to ever to have a problem.
ForStatsFiles is where files that are created by "DataPageStats.exe" go to wait to be imported into DataPage. If they are in FSF, then that says that they aren't in the DP database, and
SHOULD NOT BE deleted. Run the DataImporter by right-clicking the DI icon in the task bar and selecting "Check". This should send them to the database and transfer them to ForHandledFiles.
Every year, I archive them, and then ZIP them. My database after almost 5 years, from 2 computers, is roughly 2.5GB, and my backup XML files, zipped from one computer, total 94.8MB. It's worth keeping those XML files backed up, IMHO.