It's in the attack. In some songs I hammer down and really push down with my fingers.
Some I just chill and have more finesse. With bass, a LOT of the tone is from your fingers and where you're hitting the strings. Hence why you can go from one sound to another without making any changes to your gear. You just change your technique.
The closer to the bridge you play with your fingers, the more treble sound you'll get. Closer to the bridge and you'll get more bass. When I want mellow deep sounds I pluck actually on the fretboard with my right hand.
I'm not the biggest fan of flatwounds. But if you're going for that sound and getting some buzzing, it'll help get rid of it. You can't get that clank with a pick because 1) you use a pick and you pluck vertically. 2) With your fingers you're coming a the string horizontally. If you want to do that with a pick, you'd have to turn your pick 90° and push down towards the body of the bass. Not gonna happen.

