Several factors go into what a pickup sounds like.

Guitarsmith Richard Stanley says:

There's an array of considerations in voicing pickups. I'll give you the short version of what the factors are:

• Turns count — how many turns of wire in the entire coil. Average pickups have about 8,000 – 10,000 turns, approximately a mile of wire. This affects voicing directly through the inductance which varies as the square of the turns count.
• Layup style or pattern — whether you lay-up the wire evenly, back and forth, layer and skip back, do a skew or honeycomb winding. Those have different voicing properties.
• Choice of wire — most standard pickups are wound with 42 gauge wire. I also use 41, 41.5 and 42.5 gauge wires — all in single coat or double coated insulation. In general, if you want a brighter pickup, you use a heavier gauge wire, with heavier insulation.

There's a whole evolution in pickup design waiting for exploration by people in this business. For the most part manufacturers have been coasting on 60 year old design concepts in this department.

To read more of Richard's thoughts on this subject, see DRG's interview with him.