I don't know that can be stated categorically. By that logic you could use one coil design and base a dozen different pickups on it each with its own preamp and EQ curve. The only thing the coil would do in that scenario is sense the string vibration but that wouldn't explain why different active pickups use different magnets or guages of wire. So I would think that it's a combination of the magnet, gauge of wire, number of windings and a preamp to shape the final product. The real question would be to what extent the preamp shapes the final tone? Is it tranparent or not?