Tonymead60, I must agree. Positive attitude, a renewed mind, and prayer are powerful mental abilities for triumphing over adversity. I know you've heard the quote "Life is 10% what happens to us and 90% how we react to it." Thanks for you comment.
Mental ability is more beneficial. This had been demonstrated throughout history. Look at what happened with King Philip's Armada. What about the invention of guns? and many more... But if you're talking about physical competition like martial arts or boxing, wits alone won't give you victory.
It's not possible to pick only one as both attributes work together and one cannot work without the other. For example, every physical action can not be executed without first having a mental thought of conceiving the idea. Every physical action first begins with a thought. You could have all the mental ideas for something but it is absolutely useless if you don't have the physical attributes to materialize the mental idea.
Cognitive/intellectual - no doubt about it if you ask me. There may some specialized circumstances, roles and/or lifestyles that might -*might*- credibly argue for the other - athlete, inmate, furniture mover - but overall, you can very well use your mental processes quite effectively with almost (or even absolutely?!) no physical strength or skill.
It depends fully on the circumstances. If you're confronted with a falling tree, the physical ability to leap instinctively out of the way will save your life. If you have to solve a business problem, then you have to be able to think it through.