The pulse is stronger in the carotid artery than the brachial artery due to its greater size and greater blood flow. The carotid artery delivers blood to the head and especially the brain, so it must deliver a bigger percentage of blood flow. The brachial artery delivers blood to the arm which is at rest much of the time. The brain requires enough blood flow and oxygen that it is supplied by both the carotid arteries (2) and the vertebral arteries (2) as well.
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Ideally to get more information about any potential risk you may want to consider health screening and talking to your primary health physician. I found out that there is preventive screening for cartoid artery disease. Check out the related linkbelow.
Because the carotid artery (in the neck) is nearer to the heart than the radial pulse (in the wrist).