Sorry, for some reason I didn't realize one important factor here at play.
As others mentioned, there are several things more that should be considered in the comparison. By photographing the same target with 55 mm (17-55), you are giving a considerable edge on the magnification for the APS-C lens. My suggestion would be to match the Field of views first, (70 mm FF ~ 44 mm APS-C) and check the results again.
However, even this isn't fully comparable since the maximum reproduction ratio of the lenses differ quite a bit (24-70 goes to 1:3.45, 17-55 to 1:5.9). Take the closest focusing distance of 17-55 - or a little bit further - and test both lenses at suggested focal lengths there, now both lenses should be able to focus there with the same field of view.
Then, there are some hints on the 24-70 @2.8 photo that it is slightly out of focus (on your earlier article). The pincer seems to show some greenish hue around the edges as well as the paper, which suggests that the lens might indeed have front- or back focused. Additionally, there is some haze all around the image which might be because of insufficient spherical aberration correction (which would mean some lens element has moved), or again that the lens has not been focused to the right place.
Due to lack of other objects in the 24-70 photo, I can't see where the lens might have focused. And because of the long shutter speed, it might also be that something simply moved during the take, blurring some of the details. Try using a shorter shutter speed too (1/500 perhaps) and add something like a plank to the scene so that it is easier to determine that if the lens focused wrong, where did it actually focus then.
I suppose you used the Central AF point on both lenses. Be advised that the area covered by the AF point is different between full frame and crop body, and that the AF point might not look exactly at the same direction the view finder suggests (this has been rather annoying with macro work occasionally).
Hopefully you get something useful out of this post.
EDIT: Additional question: does the 24-70 have a UV filter in front of it? If so, is it a quality filter?