Precisely what SHOULD be true, but which is not. Why? Because FF lenses are intended to fit on two formats (FF, APS-C) but were designed for the larger one. Simply the inability to make FF digital sensors for so many years caused the FF SLR manufacturers to make digital cameras with the smaller APS-x sensors so they could sell digital cameras.
We have SOME lenses made for APS-C format which have some great resolution figures, but for Canon they really want folks to want to buy their FF designed lenses...APS-C is, for Canon, more of a 'for amateurs/snapshooters' format size, and they price EF-S lenses accordingly. And the resolution numbers, while great, are not that great as one might expect for lenses made for a smaller format.
Fair point and relates to the charts I posted earlier since both are based on the same FF lens. I know lenses designed for my Olympus m4/3 achieve higher resolution than FF lenses generally do on crop sensors. I believe, at the current state of lens design, that the 60+ % advantage FF has over crop (especially Canon crop which is a tad smaller) has yet to be overcome by lens design, but really good smaller sensor lenses can be plenty sharp. As Ken R. notes, how sharp do you need? I'm impressed so far by the sharpness I'm getting on my Olympus EM-10 but have always been impressed by the insane sharpness of even cheap glass on my 6D. All great tools - I suspect the photographer at the right place at the right time with a creative vision will bring home the best shot regardless of sensor size.

