Nikon got in first on the professional market. Then Canon stole their dinner with SLRs for the masses. Nikon responded by making some cheap and fairly nasty cameras to play catch up. By the AF era both companies made excellent professional cameras, as well as some plastic not-so-fantastic rubbish. The digital era has seen both manufacturers looking like dinosaurs while Fuji, Panasonic and Sony invent new rules.
I agree, but I think the story goes more or less like this:
Canon was very focused in stealing Leica's rangefinder market share with more economic camera bodies of good quality. In optics they were very focused in competing against Leica for the M39 threadmount rangefinder lenses, patenting their new lens designs worldwide, sometimes forcing Leitz to use different optical designs because of this. A good site mentioning this is
http://www.taunusreiter.de/. You can read in many leica-thread-mount (LTM) forums or sites how good are Canon LTM lenses were in the 60s.
Nikon, meanwhile, saw that the future was in the 35mm SLR, not rangefinder, and devoted to preparing a 35mm professional SLR system, preparing a complete line of lenses for it's introduction. Nikon was a conservative manufacturer and they tried to incorporate the best and tried-and-true mechanisms available by then. That's why, for example, the shutter of the Nikon F is exactly the same of the then-current Nikon rangefinder. If they had a great shutter, why change it? There was nothing new on the Nikon F camera itself -- instant return mirrors were already available on the Asahi Pentax; bayonet mount and interchangeable viewfinders were already available in the Exakta, etc. etc. But the Nikon F was a careful, well-balanced combination of the best technologies available, and with the highest build quality possible. Plus it introduced the concept of the "system", and it was introduced with a complete lens line.
At the same time the Nikon F was introduced, Canon introduced the Canonflex SLR which had a very incomplete lens system; only two lenses had automatic diaphragms (!) and it was introduced with NO WIDEANGLES (!!) Meanwhile, Canon had all sort of lenses for LTM rangefinders.
It was obvious that Nikon was fully commited with the SLR while Canon did not believe in the 35mm SLR so much. The Canonflex is a good camera but mediocre for Canon standards. Canon could have done a much better camera by then, if they would have decided to fully devote their resources to it. It appears that the Canonflex was a rushed project created just as soon as Canon learned that Nikon were preparing a SLR...
Now, thanks to the Nikon F, Nikon got the professional lead. Meanwhile Canon saw SLR sales rise during the 60s and then focused on beating Nikon with a next-generation pro camera. This also meant developing SLR lenses of top quality and I would guess they invested A LOT of money into optical R&D since for the introduction of the F-1 in 1971 they came up with high technology, high-performance lenses that got stellar reviews in lens magazines and in independent tests.
Now, the pros were already using Nikon and with Nikon releasing the excellent F2 camera, they had no reason to bother switching to another system (and thus having to sell all their lenses, and accustom to a system with an inverse focusing and lens-mounting way.)
Now, in 1976 Canon releases the AE-1 and changes the camera market forever, since it opens the 35mm SLR to a wider public. They get a lot of profit from it and become a very powerful company that enters other business like computers.
In 1985 (?) Minolta releases the Maxxum line and suddenly Minolta is a market leader, and pros start to use the Minolta system. Nikon, always a very conservative company, decide to use the same type of system for their pro AF camera -- lens motor inside the camera body.
Meanwhile, Canon, already a bigger company than Nikon, decides to "bet the company" and devote fully all their camera and optical resources to create the best AF system possible. The result is the EOS system, which was introduced with lenses including an EF 300/2.8 lens with fast ultrasonic focusing and outstanding optical quality. Any pro photographer who really could benefit from a fast and reliable AF system switched to Canon, and they did switch to the EF system in masse.
The rest, as they say, is history.