Single coils are brighter. Humbuckers have more mids and lows and less highs. That's it. They both sound natural and "organic" (what's organic sound like, a house plant?)

Pickups are electronic, not organic.
Humbuckers are just two single coils, usually wired in series. A jazz bass with both pickups on is also like a humbucker in parallel, only the coils are farther apart.
Also single coils hum, so if that bothers you, you might want to wire up the switch for series/parallel. Parallel wired humbuckers sound very similar to single coils, but without the hum.