I'm a professional photographer by trade. I have both Canon and Nikon gear in house.
I started 20 years ago with Nikon, switched to Canon for their 1D series back in 2003 (and for lenses like the 135mm 2.0 and 200mm 1.

, and switched back to Nikon for their D3s line in 2010 when it became clear it was an astounding camera. (This was also after several years of bad experiences with the 1DmkII and 1DmkIII professional cameras).
As a result, I haven't purchased any Canon gear in some time, but - by all accounts - they're top level camera, the 1Dx, is back up to being just plain awesome.
I would not say any one camera manufacturer is definitively better across the board. Each has awesome pro-level gear and incredible lenses. Each has great feature sets. Nikon just released an enthusiast level DSLR the D5300, that has integrated wifi (something that should have been in all of their cameras about five years ago). I don't believe Canon has a DSLR with integrated wifi yet. On the other hand, Canon updated their external flash control systems with a wireless radio system recently, which is much more reliable than the IR based systems previously in use. This is a feature that Nikon does not have and could certainly benefit from. Canon has also recently innovated with a new form of AF system they are calling "dual pixel AF" which allows for MUCH faster autofocus from the live video stream when using the camera to record video or in "live view" mode. I believe this is currently only in one camera, but I would expect it to be standard in the future. On the other hand, Nikon has been eating Canon's lunch in high ISO performance for the past few years (an area in which it used to lag notably) and has also blown Canon out of the water in full frame DSLR offerings (an area in which Canon was first to enter the market).
Ultimately, my suggestion is to determine what exactly you would like to be able to do with the gear (as that can narrow the field as to what you ultimately NEED to purchase), try both brands (renting is a good option) and see which feels better in the hand and which interface makes more sense. Since you're going to be (hopefully) using these cameras a lot, I usually recommend the one that makes the most "sense" as you look at it.
Also, rather than looking at a full DSLR ... there are new mirrorless offerings from various manufacturers which are extremely good. The Nikon 1 series is rated very highly. They are still fleshing out their lens lineups but the AF is super fast and the image quality is very good. Certain models can shoot 4K frams @ 60FPS for 1 second, making for some fun action sequences. Also, Fuji has an excellent line of cameras - one in particular, the x100s has been received extremely well.
Just some thoughts ...