"여자아이가 날고 싶어해요."
Translation:The girl wants to fly.
싶다 is a bit stronger, like 'it is certain that a girl wants to fly'. 싶어하다 is more like 'she seems to want to fly'. Though the actual difference is very small. It is important to remember, that 싶어하다 cannot be used when speaking about oneself. '내가 날고 싶어해' would be rather awkward.