Needing someone means saying "I can't live without you." Wanting someone means saying "I can live without you, but I choose not to."
needing means you're dependent on the other person, the power lies with them. whether or not they reciprocate your feelings can make a huge impact on you (mostly negatively if they do not feel the same way for you)
whereas in wanting a person, the power lies within you. you don't need them, but still you choose them. whether they choose you or not.. you'll be fine.. with or without them! (of course if don't reciprocate, one might feel bad but it won't be the end of the World)