The DxO Mark scores are misleading, but that doesn't mean the gap in performance isn't real!

Several Nikon bodies (D800, D600 many of the D3xxx and D5xxx series) are using Sony Exmor sensors which feature a cutting edge ADC/read noise reduction system to achieve massive gains in dynamic range compared to Canon sensors, which are designed and fabricated in house.

This is reflected in the DXO "landscape" score, but is better demonstrated by looking at the dynamic range graph:

(c) DxO Labs

As you can see the gap in dynamic range disappears after ISO800, this is where it moves from being read-noise limited (where the D810 is significantly better) to being photon-noise limited, where both cameras perform similarly as photon noise depends mainly on how many photons you capture, which is determined by sensor area.

The DxO low light score is massively skewed towards the Nikon camera as it considers colour accuracy as well as noise. Canon colour accuracy is slightly lower due to a design decision to optimise for sensitivity and performance under flourescent lights. The signal to noise ratio graphs tell a more accurate story:

(c) DxO Labs

The measured results are very close, which is exactly what you'd expect if noise is photon limited since two sensors of equal size will capture the same number of photons. Signal to noise ratio isn't the only concern and people will often qualitatively pick one over the other. But the fact remains low light noise performance is similar.

What is not similar nor open to interpretation is the gulf in shadow noise at low ISO. Canon are invested in sensor production so lack the ability to "shop around" for the best model, so it's unclear when they will be in a position to turn the situation around. Low ISO dynamic range is just one on many factors that make a good sensor (or camera) but if it is important to you then it may be worthwhile switching, as Canon have not moved on this front for quite a few years now, they are either unable to improve (due to manufacturing limitations or patent issues) or don't regard it as a priority (or both).