Man is the only creature in the entire universe blessed with a body and a mind. It is this, which makes him the crown of creation. While a healthy body is necessary, but in absence of a healthy mind, he is no longer a human being, but is more akin to an animal. Thus in my opinion a healthy mind is more important than a healthy body.
While the body is subject to ageing, the mind is not. Thus a healthy person may with a passage of time, grow old with age. On the other hand, the mental faculty of a person not only increases with age, but he becomes more mature, wiser and experienced.
So, in my opinion, a healthy mind plays a very significant role in one’s life to conquer all the barriers and challenges.