The physical difference between a spherical and elliptical stylus is the shape of the diamond. An elliptical diamond allows for more detailed sound quality, as it fits better within the groove and therefore has more contact area with the groove itself.
If however you are a DJ and enjoying scratching, a conical is more robust and better suited. For most modern recording, it is difficult to tell the difference, but if you dig our and play something like and old soul record from the 60's or a 78rpm, you will almost certainly get more depth using an elliptical