Both were Parselmouths
Harry talked to snakes for the first time when he went to a zoo along with his cousins.He discovered this talent when Professor Snape was teaching Defense against dark arts in the movie Harry Potter and the Chamber Of Secrets and Harry defended himself by talking to snake unconsciously. His talent enabled Him to unlock the chamber of secrets Voldemort too knew the language of snakes and maybe this was the reason why he had made Slytherin snake and Nagini his pets.
Both Had Interest In Dark Arts
Though Harry never misused his skills he had extremely well knowledge of Dark Arts. He mainly used to learn the dark arts as a defensive mechanism.Voldemort was a pure genius of dark arts who used it to rule the world. They both had an interest in the subject of dark arts, but they used them for different purposes.
