From looking at other peoples Canons, and my own Nikons, I'd have to say that if you take the closest comparable lenses, there might be more difference in sample variation than there is, on average, between the two lens lines.
Or, at least, there used to be. I recently bought the Nikon 14-24 and the 70-200 f2.8s and they are terrific lenses; I doubt that Canon can match them simply because (maybe) the Canon lenses are older design/technology. I don't doubt that Canon *could* match them, and probably will. One thing, carrying the new Nikons around is like carrying a sack of bricks.
As far as primes go, don't forget that Zeiss makes prime lenses in Nikon mount (but not Canon) and they are supposedly quite good. (And perhaps you could adapt the Nikon Zeisses to Canon?)
Canon, if you listen to the talk, has for a long time been weak in wide lenses, and exceptionally strong in long IS lenses and shift lenses. They are now probably matched in that by the new Nikons.
One question about Canon -- can the same lenses be used on both the FF and cropped-frame cameras? They can on Nikon, although, of course, with different FOVs; and that's actually an interesting strength.
But, generally, IMHO, this is a question of how many angels can dance on the head of a pin; each brand, along with Leica, Hassy, etc., is used by one of another of the greatest photographers in the world. If I were you, I'd buy on budget, ergonomics, personal fit, and so on. The brand ain't gonna make much difference in image quality, and people who tell you that it will, are generally people who are hoping their equipment will make them into good photographers... 8-)