The force required to start a box moving is higher. Friction is defined by the coefficient of static friction, and the coefficient of sliding friction.
The coefficient of static friction is always higher, which means that it takes more force to get an object moving than it does to keep it moving.
A simple expression relating the weight of the box to the frictional force is:
F - uN, where
F = force required to move the box
u = coefficient of friction
N = normal force (the force that the object is applying to the surface due to gravity).
If the box is moving along a horizontal surface, then N is the weight of the box. If the box is moving along an inclined plane, then N is W*cos(angle of the plane).
u = the coefficient of friction. Use the coeff. of static friction here if you want to calculate the force to get the box moving. Use the coeff. of sliding friction if you want to calculate the force to keep the box moving once it starts sliding.
Hope this helps,