When the field produced by field winding is changed a back emf produced. This back emf acts as a resistance and limits the current. But during the steady state condition of field the field winding have no back emf. Therefore we need a high resistance in the field winding to limit the current.
On the other hand, armature winding produces no back emf at rest. As the speed increases the back emf is also increased. During the running condition the back emf produced by armature winding limits the current. So we don't need a high resistance of the armature winding.