Which is healthier, ghee or first-press olive oil?

I have ME/CFS and need to follow a healthy diet. I am interested in both the Ayurvedic diet and the Mediterranean diet. The first uses ghee for cooking, the second, olive oil. Can one be considered healthier than the other?Which is healthier, ghee or first-press olive oil?
Personally i would say olive oil is much healthier as ghee is a clarified butter and does not contain the many health benefits of olive oil. Lowering choleterol, keeping your heart healthy etc is well documented when it comes to olive oil.