It's also worth mentioning that lenses designed for crop cameras use tighter tolerances in manufacturing which results in higher image quality (the parts are smaller so this is easier) so generally a lens designed for crop will perform better than a lens designed for full frame. The 17-40mm L is designed for full frame and performs nearly identically to the 18-55mm kit lens, but is more expensive and worse in nearly every way (though it's color and contrast is said to be slightly better, I don't really care personally).
Not entirely sure what you mean by "perform better", but to the extent you're right re image quality, it's only true if you compare the lenses on a crop body, as Neuro's link demonstrated; lenses designed for ff bodies work better on ff bodies, and the comparison tool at the digital picture repeatedly shows that any given ff lens performs better on a ff body than it does on a crop body; it may also show that ff lenses on ff bodies perform better than their crop equivalents on crop bodies. For instance, many a reviewer/commentator raves about the sharpness of the EF-S 60mm macro which, in comparisons, seems to perform better than the 100mm L on crop bodies; Roger Cicala's blurb on the lens says it's one of the rare lenses that make him wish he used a crop body. And it's certainly an excellent lens; but as I recently found out the hard way (i.e., I bought one, though the digital picture would have demonstrated the point had I bothered to check), while it may be light and convenient, it's certainly not as good as, let alone better than, the 100L on a ff body.
As for "tighter tolerances," even if that's true, something is evidently making a lot of reviewers complain about autofocus accuracy on the Sigma. Fantastic image quality is all very well, but you won't notice it when the focus is off. Have those reading this had problems of focus inaccuracy with the Sigma?