Speed Vs. Power

What is more important, speed or power? For me, it's speed. Don't get me wrong. I'm not saying you can be weak and prevail. And I don't consider myself exceptionally fast. I have a relaxed method of movement and contract the muscles at the moment of impact and then relax. I was talking with a student about body language and I explained that if you look closely at an opponent, you can see tension in the body before it attacks. I have spent countless rounds of shadow boxing in the mirror to study my body, so that I don't have this give away. How effective is it to be able to punch through a brick wall if you can't hit somebody? The human body is delicate and doesn't require much to hurt it if you hit it right. People think that you have hit people hard and you don't.