If I happen to think of it tomorrow, I'll do a quick-and-dirty comparison.
I thought of it.
There're four attached images from two different exposures. There's one each of the full frame and one each of a 100% crop. The one is with the 400 f/2.8 IS II, the other with the 70-200 f/2.8 non-IS at 200. Both were shot handheld from the same position, and both were exposed at 1/3200 @ f/2.8 @ ISO 100. The 400 is as-is; the 70-200 is cropped to the same field of view as the 400 and then up-scaled to the same dimensions as the 400. Oh -- and it's with the same 5DIII. Autofocus, center focus point on the ColorChecker. Both lenses I've previously AFMA'd with FoCal.
I've done minimal post-processing. Exposure and white balance I normalized with the ColorChecker Passport you see. There is no noise reduction of any kind. I did my usual high pass capture sharpening, the exact same amount, to both files before scaling, and I similarly did the exact same output sharpening to both the scaled-down full-frame shots. The initial TIFFs I output to BetaRGB for all the Photoshop work; at the end, I used ArgyllCMS to do the same gamut-mapped perceptual conversion to all four to sRGB. That's particularly relevant for this shot, as the soup can's red is outside of the sRGB gamut.
I leave it as an exercise to the reader to figure out which is which -- if you can't tell, you need glasses. Though, I will note, if all you're going to do is twit a pix to FaceSpace, the 70-200 does hold up remarkably well for such uses.