The next thing is that apparently EF lenses have better image quality than the EF-S variety but when looking at the price, the EF-S is quite a bit cheaper. Now the question is, does the EF indeed have better image quality, and if so, is the quality difference so much as to warrant the price?
All other things being equal, it helps to visualise what really happens when you use an EF lens on a crop body. The lens projects a picture that is wide enough to cover the 36 mm "full frame" sensor, but on a crop body you only use the centre 24 mm section of this image (and similarly in the height direction too).
This means that if an EF lens "looks soft in the corners" on a full frame body, it might look relatively better on the crop sensor because you are not using that part of the projected image (it is "cropped", i.e., the light is absorbed by the matte black coating inside the crop-sensor body).
So as you can see, this will depend entirely on the specific lens. Some EF lenses might only "go soft" right in the extreme corners --- these lenses may look great on a crop sensor body.
If you want to really get into this discussion, though, you also have to keep in mind the design parameters for the lens. Example: I have a Nikon 105 mm f/4 macro lens from about 1977 --- obviously this is a "full frame" lens. Being a macro lens, its sharpness is pretty even right up to the corners (of a crop sensor, since this is all I have). I also have a Sigma 17-50 mm f/2.8, which is a crop-only lens (i.e., EF-S). This lens is significantly sharper than the macro lens, especially in the centre of the frame (do not quote me on the extreme corners, cannot give a definitive answer there at the moment). In the centre, the actual resolution of the 105 mm macro lens is only about 75% that of the Sigma.
What this means in practice: For printing, say, and A4 photo, the magnification factor for the EF lens on a full-frame camera is only about 7.75 times (to scale the image on your sensor to an A4 size page). To print A4 from a crop-sensor camera you have to magnify the image by 11.62 times. This means that if you want the same sharpness in your printed A4 photo, the crop-sensor camera must have a lens that 1.5 times sharper (1.5 times the resolution).
Since a lens design is always a trade-off between many characteristics (centre sharpness vs. corner sharpness, lens distortion, chromatic aberration, etc.), it is reasonable to assume that not all lenses are designed for maximum sharpness. So how sharp must a lens be? Well, if you are going to print, say, A4, then you know how sharp the lens must be for a given sensor size. The trouble is that the target for "acceptable sharpness" on a full-frame lens would be 1.5 times
lower than that of a crop-sensor lens to produce the same apparent sharpness in a printed A4 photo.
Bottom line: Theoretically you need a lens designed for a crop sensor body to achieve maximum sharpness (in the same size printed photo). In practice, there may well be many EF lenses that produce better overall image quality (specifically, sharper image corners) when used on a crop body, but this will probably only apply to the better quality lenses (think L). Sigma and Tamron do a pretty good job (Sigma more so) of designing good lenses for crop sensors, so I would definitely include their lenses in a comparison before blindly buying an EF L-class lens only on the assumption that this
should produce better image quality.