I think hope and fear are two very different emotions you can't really compare which one is more powerful of the two. Its kind of like comparing a carrot with a watermelon, they are both edible plant material, but they differ so widely, you can't really compare the two.
Fear is a fundamental part of being a human, it deserves respect, and needs to be felt and accepted. Suppression of fear, I believe (based on personal experiences) is one of the chief underlying causes of illness and disease in today's society. Fear has this stigma of being evil and bad, but it isn't. We need fear, we cannot run away from it or suppress it and if we so much as try it'll come back and hurt us (and believe me, it hurts like hell when it does come back).
I think hope might be a choice. One thing is for sure though, you can certainly feel fear at the same time as feeling hope, hope does very little to diminish fear. I've always lived with a lot of hope, its a wonderful warm and powerful emotion. Hope is powerful enough to keep people alive in the darkest of times. Hope gives strength and drive to keep going, against all the odds. But it doesn't remove fear.
The only emotion I have found, which you can't feel at the same time as fear is love. But even then, you can fight fear with love, because if you need to feel the fear, you WILL feel it regardless of whether you try to fight it with love or not. Its far less painful to just accept the fear and take what comes, rather than suppressing or fighting it.