DSC will show up mainly Tm and Tc. Since PA6 and PA66 have a different Tm you will be able to differentiate both. On the other hand, singling out virgin from processed is another tale. Currently there´s no way to distinguish if a given nylon have had one or more reclaiming loops, neither details about such previous process. However certain new equipment are way better when solving different DSC transitions. Of course, the expensive this equipment, the sharper.
DSC generally used for calculating the energy consumed by the fibre while heating. Surely the processed nylon will produce different curve in heating. We can differentiate using glass transition temperature and Tm.