Young Sheldon and The Big Bang Theory share similarities in Sheldon's stubborn personality and his mother's religious nature. However, Young Sheldon is set in older times in the 1980s to show Sheldon's childhood, while The Big Bang Theory is more modern. Some key differences include the use of narration in Young Sheldon, lack of laughter in scenes, and Sheldon's father appearing in Young Sheldon but not The Big Bang Theory.