Arteries at Risk

"Large" arteries and "small" penetrating arteries are both involved in stroke

The arteries that supply the central nervous system originate from the aorta or other great vessels. “Large” arteries are defined as the extracranial portions of the carotid and vertebral arteries and their large intracranial branches, which lie in the subarachnoid space on the surface of the forebrain and brainstem. These large arteries in turn give rise to “small” arteries.

“Small” arteries are the vessels that actually enter brain tissue and ultimately branch to form the capillary beds where oxygen exchange occurs. Some small arteries are short branches that supply superficial regions. However other small arteries are long branches that penetrate deep into the brain parenchyma to supply structures including the basal ganglia, internal capsule, thalamus, as well as parts of the brainstem and cerebellum.

Ischemic strokes most frequently involve narrowing or blockage of large arteries.
Hemorrhagic strokes are more equally divided between the large and small arteries.

Strokes affect the forebrain most often, the brainstem or cerebellum less often, and the spinal cord rarely 

This presumably reflects differences in the volume of tissue, and in the sizes and arrangement of the arteries that supply these regions.