I'm going to talk more about my experience vs anything technical here. If you're looking for technical and validation, check out Hoffer Photography's or Tyler Wirken's post about their reasons for changing.
Kristiaan and I have been using Canon since before we started our business. She was film and I just got a Canon because of her and my dad who used Canon most of his life (film).
Over the years we upgraded cameras and lenses and drooled over the red rings and the latest bells and whistles. Canon was good to us so we never entertained switching until some of the recent mirrorless cameras. Even then it wasn't a real consideration, just that our eyes were opened to possibilities.
If we had any gripes about Canon, specifically the 5D series (i, ii and iii) it was that not all the focus points were as accurate and sharp as the center one. Not a big deal, focus and recompose and boom. We were fine. And every once it a while, images we were certain should have been in focus weren't...sadly we assumed it was user error. So we kept at it.
Then we started to hear about the Nikon D750 and all the wonderful things it could do - dynamic range, focusing, cost etc. It took me a few months but I eventually rented it (Nov 2014), after renting the Nikon Df. Within the first 30 minutes of shooting getting ready images at a wedding I was sold. I felt as if I was in focus before I even had to think about it. The responsiveness in low light as well as the accuracy and speed of focusing blew me away. To the point where I was almost sick to my stomach at how inferior Canons focusing felt afterwards.
Then I started to pixel peep (zoom in at 100%) and edit files, WOW! I had more room to be creative with dodging and burning, colors and recovery if anything was over or underexposed. Overall my image just looked, and actually were, sharper.
We priced out what it would cost us to change and what we could potentially make selling our Canon gear. Surprisingly we would come out making more by buying all new Nikon and selling our Canon. One huge saving point though was that we went with Godox V860n's instead of Nikon SB-900s. We owe a huge thanks to Joseph Victor Stefanchik for the recommendation - although he really did recommend Cheetah flashes. We just went with something a few $$ cheaper.
As far as lens recommendations we followed our wedding photographers advice on ShotKit. Our setup (see below) gives us lighter/smaller lenses at a lower cost which is a huge win.
The Nikon D750 has not disappointed so far. Its also lighter which makes a 12 hour wedding feel a little better on the hands at the end of the day. Well there is that sometimes flare issue... We have experienced it with one of our four cameras and have not sent it in yet.
So final thoughts? More responsive and accurate focusing, better focusing in low light, cost less, lighter on the hands.
What we own:
4 x Nikon D750
2 x 35mm f/2.0D
2 x 85mm f/1.8G
1 x 60mm f/2.8
1 x 105mm f/2.8
1 x 50mm f/1.8
1 x 24mm f/2.8
8 x Godox V860n