It might help understand the DxO tests and what they mean. Which basically means you should ignore the overall score and look at the components contributing to it.
The "colour depth" score I believe is influenced in large part by the strength of the colour filters. Stronger colour filters lead to better colour separation, at the cost of more light lost. Canon have generally used weaker filters, especially the red one, and can give noticeably colour differences. Unless Canon have changed there, this isn't a strong spot.
The "dynamic range" score appears to be derived from the maximum at low ISO, where Nikon/Sony/Pentax have in recent times been doing something to get more range at low ISO. Canon so far has not. So this is another weak area for Canon.
Finally, there is the "low light ISO" score. I believe this is a simple measurement of signal to noise level. Where it may deviate from practice is I do not believe it has consideration for the character of noise. That is, some types of noise patterns may be more objectionable even if it is of the same nominal level.
Overall... regardless of how the sensor performs, I wouldn't expect the 5D3 to score well unless Canon are doing something radically different in the sensor from the past, which as far as can be gathered so far, doesn't appear to be the case.