First off, the support. I was travelling through Asia (Thailand, Indonesia, Philippines) a few years ago with my Nikon. I started having problems with my shutter closing halfway through an exposure and tried everything I could think of. So I tried finding someone who could look at it in Thailand, no luck since Canon was the dominant brand there. Got to The Philippines and Canon was everywhere there as well but noone would have a look at my Nikon
Finally caved and bought a 5d2 and literally gave my old camera away. Haven't looked back since.
Second, I like the skin tones sooooo much more on my 5d2 than the comparable D700, D800. People just look more alive and vivid rather than pale and sickly on the Nikons. Sure you can tinker in post, but I prefer not to do too much work in post anyway.
Third, is Magic Lantern. There is no equivalent on the Nikon side of things and since I shoot a lot of video while travelling, it really comes in handy and I can't imagine not being able to use it anymore.
Finally, there really isn't a better all around camera than the 5d3 in my opinion. I am upgrading to it in the near future and if I had gone Nikon, I would be stuck with either a D800 or D600. Since downgrading is out of the question, I wouldn't touch the D600. The D800 also feels slow, sluggish, and I don't like having to upgrade my computer to handle the file sizes in LR.
Although there are some things on the Nikon side such as better dynamic range, the creative lighting systems, better ergonomics (subjective), and a slightly better shutter sound (really subjective) that I want, I am happy with my Canon.