How can we differentiate between upper motor and lower motor neuron lesions on the basis of babinski's sign ?
Short answer : If the Babinski sign is positive in adults, it indicates an upper motor neuron lesion.
Long answer :
The plantar reflex is an interesting reflex since it has two physiological responses. One in kids 1-2 years of age and another in the rest. It is one of the primitive reflexes that are present in infants but are cortically inhibited later in life.
The primitive response to the plantar reflex is extension of the hallux and fanning out of the toes. Once the kid is around 1-2 yrs of age, the corticospinal tracts are fully myelinated and this primitive reflex is inhibited leading to the flexion of the hallux.
Extension of the hallux is regarded as a positive Babinski sign while flexion is sometimes called negative babinski.
So in an adult, due to cortical inhibition of the primitive reflex, the plantar reflex should yield flexion of the hallux. But if it pathologically shows a babinski positive, it indicates the absence of cortical inhibition - an upper motor neuron lesion. This might be a serious neurological issue and you'd want to do a CT brain, CSF study or an MRI spine to localise the lesion.
On the other hand a negative babinski in kids who should be showing the primitive reflex, may be showing signs of spasticity. This should direct us towards progressive neurological disorders like cerebral palsy.