Pickups can shape the tone more than any other feature.
Humbuckers give a hum-cancelling fuller sound and take well to gain. They can sound dark in clean tone under certain situations.
Single coil pickups give that 'bell like' chime and excel in delivering clean tones. With gain they will introduce hum, however there are plenty of noiseless versions now on the market. They can sound sharp at times and don’t give the same clarity as humbuckers when driven.
P90 Pickups are essentially overwound single coils. They have a distinctive growl and biting mids. They can suffer from hum too, but are great all rounders.