A concave mirror of small aperture produces a sharper image because of the difference in the focal length. As the aperture of a lens (concave or convex) increases or decreases, its focal length also varies. The main reason for this is that in case of large aperture, more than one focal lengths are formed from the same focus. (this problem is called spherical abberation)
Thus, a smaller aperture mirror will be free from spherical abberation, and produce sharper image.
Same goes for lens:
(smaller aperture lens)
(larger aperture lens, having many focal points)