Originally posted by Digitalis in some ways full frame can be more demanding on other aspects of lens performance, issues such as vignetting, (or fall off for the more technically discerning amongst us). flare and optical aberrations can often be exacerbated by the increased image recording area.
I don't want to go too far into this as it is OT here.
You're right if you're comparing at a given f-stop and focal length. This is why this statement is a common one.
However, if you compare equivalent lenses (the FF lens then has a longer focal length and a higher f-stop; but still the same aperture diameter in mm and about same weight and cost) then these problems are gone.
One very simple thought experiment may help to understand: Look at the ray coming from the corner of an image passing thru the center of the lens, i.e., hitting the sensor at the opposite corner. The angle at which the sensor is hit then is defined by the field of view and independent from sensor size. More complex arguments are required to treat this fully. But FF offers better resolution
potential while keeping other problems about constant.