PI only enters cells with compromised membranes and stains nucleic acids. Thus PI is thought to be an indicator of ‘‘dead’’ cells. DAPI is semi-permeable, and its permeability depends on concentration. Too high concentration of DAPI can stain live cells. Both DAPI and PI can stain dead cells.
The difference between the two is that the two dyes bind to DNA in different ways. DAPI binds strongly to A-T-rich regions in DNA while PI binds to DNA by intercalating between the bases with little or no sequence preference.
Hi, Hoechst33342 has the same spectral characteristics as DAPI, but is more cell permeable. It should stain apoptotic cells more brightly: https://www.thermofisher.com/order/catalog/product/V23201
Both of these dyes are typically used for staining "dead" cells. This population is distinct from apoptotic cells which are "dying". Typically, TUNEL assays or Annexin V staining are used to directly measure apoptosis.