Well, lenses with spherical elements can have spherical aberration which often manifests itself as a cloudy, low-contrast image (since an ideal perfect lens shape is not quite spherical, but spherical lenses are MUCH easier to make). In the 150 years or so of lens design, lens designers have figured out ways to use multiple spherical elements to reduce spherical aberration, so it's not as big of a deal than it used to be. Still, though, aspherical elements are still necessary in many lens designs (every modern ultra-wide zoom has at least 1 aspherical element), and a quite a few high quality wide-aperture lenses have them too (the very expensive Leica ASPH lenses come to mind). Letting the lens designers use an aspherical element gives them another variable to play with to optimize the lens design, and could improve the overall quality- not only in terms of resolution, but also correcting other aberrations.
But ultimately, it will be the performance of the lens that will determine whether or not it is better or not. Having an aspherical element is not a guarantee it will be sharper. It is a guarantee that it will be more expensive though.