Since B&W film is sensitive to most visual wavelengths (there were both ortho- and pan-chromatic films), as are color sensors and even single color (monochrome) sensors, then APO lenses provide a theoretically superior image, giving a more uniform (faithful) response to the incoming light.
As for our eyes, we definitely do not have APO eyes. Red and green wavelengths are focused to different points into our eyes (depth-wise). This fact led to the development of a "Duo-Chrome" test during refraction to better optimize imperfect glasses.
However, our corneas are aspheric in shape (until mucked up with laser surgery, which typically turns it spherical). In fact, even trilobites had aspheric-shapes terminating each compound element.