Get your brooms, boys and girls…I declare shenanigans!!
...it seems that DxO's measurements don't match others...
Wouldn't be the first time. Notably, they delcared that the 70-200/2.8 IS II was not quite as good as the original 70-200/2.8L IS which it replaced, a finding that completely contradicted everyone else who tested or used the lenses. They were called on it in the review comments, and they defended their test results. A year or more later, they quietly updated their original data and results to show that the MkII version is, in fact, the better lens. Surprise, surprise.
Comparing their actuance (sharpness) field map for the 17-40/4 af f/4 vs. the 16-35L II at f/8, where the 17-40 is sharp right into the corners and the 16-35 is soft even stopped down to f/8, pretty clearly demonstrates that their tests of the 17-40L are just plain wrong.
Compare the plot below to TDP's ISO 12233 crops
(showing the same FL+aperture comparison as the DxOMark screenshot below) which match the experience of pretty much everyone. The 16-35 definitely has some corner softness, even stopped down. The 17-40 is pretty mushy in the corners wide open, certainly nothing like the very similar sharpness in the corners as in the center that DxO shows.
With both lenses stopped down to f/8, the sharpness is pretty similar - IMO, the reason to get the 16-35 II is if you need/want the f/2.8 aperture. I went that route, and the extra stop has often come in handy, particularly with an ultrawide where the DoF doesn't get too thin (16mm f/2.8 focused at 10', everything from 5' to infinity is in focus).