The series filed winding is always connected in series with the armature and thus has to carry the armature current which directly gets decided by the load.
Thus the current passing through series field winding is of high level.
The voltage drop across series field winding gets added to the voltage drop across armature winding while deciding the back emf. This voltage drop must be very small.
Hence as the current through series field winding is high, in order to keep voltage drop across it to a small value, its resistance is very low.
On the other hand, the shunt field winding is directly connected across the rated supply voltage hence to limit current through it, resistance is very high.