huh?
Actually FF lens have better sharpness, less corner vignetting on crop body, because of using the sharpest centre area of the lens, that is if both have the same pixel density of the crop and FF sensor.
Some FF lens are design for FF film, so the image quality doesn't turn out well on crop sensor due to sensor's reflective nature. But the same would happen on FF sensor also.
But some focal lens would render it not so useful once it's on crop body as it's no longer as wide, e.g. 28mm become 28x1.5 = 42mm on crop body.