To put it in words rather than pictures (though the latter are more illustrative), in my experience from actually using the 28-300L (as opposed to reading reviews), it delivers the same IQ as the 24-105mm across the whole 11x zoom range. Like the 24-105, it's a bit sharper at the wide end than the long end, but the wide ends and long ends of the two lenses, respectively, are very equivalent.
Are my TS-E 24L II, 35L, and 70-200/2.8L IS II sharper? Yes, but then, they're all sharper than the 24-105, too, and none of them have the extensive zoom range. The drawbacks of the 28-300L as a walkaround lens, compared to the 24-105, are weight, size, and cost...not IQ.
My 2¢, after shooting with the 24-105 for a couple of years and the 28-300 for several months, on three different bodies.