I have had both the D610 and the D810 and while the 610 takes amazing images when used with top glass, there are some really big difference that I found were worth the price difference. The clarity of the viewfinder was significantly better in the 810 and the 610 has what to me is an annoying green tint that was hard to see in daylight shoots. Although I did not use either primarily for video, the 810's live view is much clearer and versatile than the 610 if that matters to you.
All that said, I have no experience with Canon at all but I chose Nikon because I did have some experience with them way back in the day and loved the quality of the lenses I had. If you do choose the D810, I think you'll be very happy if you choose the lenses that suit it. I have the 14-24 and the 16mm 2.8D fisheye both of which work really well with the 810.