It all depends what are the tools you dispose.
Infrared analysis will tell you easily whether it is ABS or PP. If the material is too thick for a transmission measurement, you can always use ATR (Attenuated total reflectance), which allows you to measure some microns inside of the solid. Raman would do the trick as well. For the three methods, the CH and CH2 group spectra will only appear in PP. On the contrary, ABS will show aromatic rings, which are active at different wavebands which allow to see the difference.
Thermal analysis (e.g. differential scanning calorimetry) would also be useful; it is destructive but you only need a tiny piece. As ABS and PP have different glass transition temperature and melting point, it is possible to distinguish them.