Here’s a rough-and-ready comparison, from a guy who’s mounted at least a half-dozen cartridges with a now ancient Dennesen Soundtracker --
Conical styli are inexpensive and easy to set up for pretty good, easy on the ears sound but they come up short on detail, imaging and air.
Elliptical will give you more detail, imaging & air than spherical/conical, and they’re still reasonably easy to mount and align onto the arm.
Chakster’s list of advanced shapes can all get you close to nirvana but set up and alignment become critical. Stylus rake angle has to be right on, which means you have the tone arm properly leveled (which can be a ticklish process). This includes having to account for how much the tracking force might deflect the tracking angle. It the adjustment is off, say hello to distortion, particularly as you reach the dreaded inner grooves....
Conical styli are inexpensive and easy to set up for pretty good, easy on the ears sound but they come up short on detail, imaging and air.
Elliptical will give you more detail, imaging & air than spherical/conical, and they’re still reasonably easy to mount and align onto the arm.
Chakster’s list of advanced shapes can all get you close to nirvana but set up and alignment become critical. Stylus rake angle has to be right on, which means you have the tone arm properly leveled (which can be a ticklish process). This includes having to account for how much the tracking force might deflect the tracking angle. It the adjustment is off, say hello to distortion, particularly as you reach the dreaded inner grooves....