Alnico Magnets:
A-2: Warm, vintage tone with slight compression. Looser bottom end that can become "boomy", with dense guitar bodies such as mahogany. Lower perceived output, and usually wound less for a more vintage tone.
A-3: Open, balanced tone, more high end feel and a tighter bottom than A-2. A little airier tone (am I describing a magnet, or a woman?).
A-5: Edgier, higher gain, but still retains the articulation and definition of a lower output magnet like the A-3.
Ceramic Magnets:
Usually used in applications where higher gain and a much edgier tone is desired. Can become harsh if the pickup is not constructed well, but can also have a smooth, articulate tone similar to an Alnico. Ex.: Joe Barden's Strat and Tele pickups were (are?) wound with ceramic magnets. So are some of Bill Lawrences, as are Carvin's AP-11 single coils. All are smooth and articulate, with great note definition and clarity.
There's a lot more that goes into a pickup than just the magnets alone, although they most definitely are responsible for the core of the tone. Wire gauge and number of turns make a huge difference. The method of winding the wire on the bobbin makes a big difference too. Tight, even layers of wire winds tend to give a pickup a cleaner, more sterile tone. Looser, scatter winding tends to impart more warmth and tonal subtles to the pickup. Even the build up of the wire effects the tone with winds that build the wire with a "hump" in the center of the bobbin creating thicker, warmer tones, while concave windings producing a more scooped tone. 43 gauge wire is supposed to create thinner sounding pickup than 42 gauge turn for turn (although most really overwound pickups use 43 gauge in order to fit the number of turns necessary on the limited space of the bobbin).
The more I learn about pickups, the more I realize that it's an art form. And like most art, every winder has his own techniques that result in something unique to them as an artist.
