They are almost the same, but there is a very slight difference in meaning or nuance - at least, to my ears.
With "I've been studying Spanish since childhood" there is a tiny bit more more emphasis on the fact that you are still studying Spanish now". With "I’ve studied Spanish since childhood" it is not quite so definitive. It suggests like the other that you are still studying Spanish now but it leaves open the possibility that at the present moment you have stopped - perhaps temporarily, perhaps forever.