Coulomb friction is one thing sliding past another, like leaves of a leaf spring, so is related to displacement and so there is an initial 'stiction' before the leaves move and the spring compresses/extends. This gives a harsh ride and prevents the tyres following the road surface, that is why no road vehicles use friction damping any more.
Hydraulic damping is related to velocity so at low velocity as the car goes over dips and hollows or cornering enables the tyre to follow the road; also dampers (such as the Bilsteins) can be tuned to give the right combination of damping force in bump and rebound and at low velocity (eg entering a corner) and high velocity (bumps) to give good ride and handling.
So hydraulics have it, get rid of friction between the spring leaves with spray grease. Regards PJB