I went to the site and compared the Canon T3i and the Nikon D4 at ISO 400. I downloaded both full-sized images from the "New Indoor (INB) 400" set. I noticed that the focus on the Nikon photo is not quite right on much of the mannequin. Look at her necklace, and you can see that only the very left edge of it is within the depth of field, and the right hand side is already slipping out of the depth of field zone, and into defocus!
Looking at the wine glass and wine cork however, the Nikon's image IS IN the focus plane, and is a slight bit crisper and sharper than the T3i image. One thing that is clear too is that, on the book the mannequin is holding,and on her wrist watch, there is a goodly amount of magenta chromatic aberration showing on the black type and the watch band shot with the Canon lens. The Nikon lens sample is completely free of that chromatic aberration. The depth of field, or focus point, in the Nikon shot, is not "quite right" on the sample photo I downloaded. Perhaps this is due to the lesser depth of field a full-frame sensor gives compared to a 1.6x crop sensor. Or perhaps it's due to sloppy work. The Nikon image appears to me to be over-exposed a slight bit as well--making me wonder how the exposure was determined. By a light meter? By in-camera meter? By histogram?
Anyway, the claim that the Canon T3i delivers "sharper images" than the Nikon D4 is a pretty broad claim. Many cameras aimed at newbies have the default in-camera sharpening set pretty high, creating that kind of point & shoot type eye-candy type of file that newbies often want. Without Photoshop, and shooting in-camera JPEG, many newbies want to have HIGH in-camera sharpening applied by default, and we can see this by looking at the dPreview camera reviews; MANY cameras aimed at beginners, like the Canon T3i, use strong in-camera sharpening. Many pro cameras use lower sharpening, which is less-destructive, and which allows the user to process the images as needed in Photoshop or CaptureOne, using SOPHISTICATED sharpening methods out of the reach of the skill set of newbies.
As to being sharper...I looked on dPreview, and the T3i seems capable of around 2,500 l/ph resolution with normal processing, and as high as 2,700 l/ph with added sharpening. They have not yet tested the D4, but I expect its larger sensor to produce higher l/ph figures than the T3i. Regardless, the D4 is optimized for speed, and high-ISO capabilities. The D4 is the Ferrari Testarosa to the T3's Volkswagon Jetta...not really a fair race, but then, we all know that.