Well, on an uncropped, photoshopped, 800x600 image, you probably can't tell the difference between an L, the kit lens, and an old Kodak 3mp digicam from the 1990s. The more expensive lenses shine when you look at full size 100% crops. Also, more expensive lenses are built better, have better AF, and generally produce more accurate color.
If all you're looking for is one good image, then you can get that from most lenses under the right conditions. What the L's give you is a combination of durability, quality, quickness and accuracy. Many of these qualities are not discernible from two side-by-side downsized shots.
As for your original question, if both lenses are stopped down, mounted on a tripod, and the lighting is great, I imagine the IQ produced by them is relatively close. However, this isn't really an accurate test of the lens' ability.
Just my $0.02.