Liquid fuel is more energy dense and throttleable, so a missile that uses liquid fuel instead of solid fuel will have significantly more range and better energy retention.
Solid fuel once ignited will continue to burn until it's empty, though limited throttle response can be achieved by clever designing of rocket casing.
Solid fuel is also more cheap and much easier to store for long time, while it's more complex, expensive risk toxic leaks to store liquid fuel.
Solid fuel missiles can also be immediately readied for a mission, while liquid fuel missiles will need to be prepared and checked before being deployed.
So ICBMs that are stored in silos for years, use Solid fuel.