What is the difference between spherical and ellipitical stylus tips?

An elliptical stylus is the generally the more expensive, better sounding option. Because of its shape, elliptical styluses follow the record groove oscillations more accurately. For home listening and for getting the best out of old vinyl, elliptical styluses are recommended.

However for some forms of DJing, the spherical stylus is recommended. During heavy scratching and back-cueing, a spherical stylus will lead to less record wear than a elliptical stylus. However, many DJs (especially house / dance DJs) still use elliptical styluses.