It’s widely accepted that the dominant hand is stronger than the other (nondominant) side. Studies from the 1950s suggest a 10 percent difference in grip strength between right and left hands.
Later studies supported a 12 to 13 percent difference for right-handed adults. Left-handed adults were more even from side to side. There was less than one percentdifference in grip strength from side to side in this group.
Shoulder strength appears to be about the same from one side to the other. Studies have not shown a significant difference in rotator cuff strength (muscles around the shoulder) from side to side.