It is primarily with shooting video where the real time autofocus performance of a mirrorless camera provides significant advantages over a DSLR. A high resolution electronic view finder is also a major benefit when shooting video and this is also provided with the high end mirrorless cameras.
But Nikon is at least two years behind Canon in producing cameras with top video performance and it is even worse considering that 90% of the third party video applications and hardware is Canon only.
Canon's FF mirrorless will be introduced to counter Sony. Nikon is not even in the race when it comes to video. I know cameras like the D810 can do a great job with video but only with a lot of attachments and external sound and video recorders and special brackets that are not needed with many mirrorless cameras.
Cameras like the Olympus E-M1 and E-M5 Mk II with in camera 5-axis optical stabilization also make stable video much easier to do and make it easy to work off a tripod. Shooting video with these two cameras, which I own, is infinitely easier than with my D810 and D750 cameras.
There is also the issue of available cine lenses for shooting video. Standard lenses have too short a focus pull which compounds problems with trying to manually focus while shooting. In terms of digital cine lenses there are 25 available from Canon and not a single one available from Nikon.
Sony and Canon are heavily invested in video and have a deep and broad base from which to provide solutions for their still cameras, while Nikon does not.