Yes, i am debating this clichee, but not in the purpose of granting the prize of "winner" or "better at something" to one or the other, but to analyze the actual differences between the two and most of all the non-specification differences which really makes a camera particular.
A brief history:
1937 ; 1917
first 35mm camera
1936 ; 1946
first SLR camera
(Canon Flex) 1959 ; 1959 (Nikon F)
Professional grade cameras
(Canon F-1) 1971 ; 1971 (Nikon F1)
Full-auto (incl. focus)
(EOS 650) 1987 ; 1983 (F3AF)
(eos d30) 2000 ; 1999 (d1)
Other historical facts:
Nikon worked with NASA providing cameras (even a digital one in association with Kodak) suited to take photos from space.
Canon made a radical change in mount in 1986 when they introduced EF mount for a new line of products. This would benefit AF function, faster aperture control, less energy usage because of the smaller motors that are placed directly in the lens, unlike other AF systems which had all the electronics in the camera body.
Nikon developed medical equipment based around precision optics.
Canon patented and introduced Eye-controlled AF (a techology used for a couple of years in a few models which was dropped. This was an unnecessary function that more often slowed the photographic process. It was never introduced in a flagship model).
Copying technologyJust like cars, photographic equipment corporations follow each other's moves and products very closely thus producing a very similar range of cameras and accessories, though some original innovations like IS (image stabilizer), processors, mounts and other techological advancements are patented and copyrighted, but are shortly after imitated by the others with a different approach which won't, in most cases, have the success or appeal of the icebreaker.
For example Canon introduced the 75-300 IS in 1995 which proved to be very useful in handheld situations, though not very suitable for sports and professional photography.
The first professional grade IS lens from Canon was the EF 300/4 introduced in 1997 which could detect panning movement (essential for sports photography).
By the year 1999 most of Canon's super-telephoto lenses had Image Stabilization (including the 400/4 and.
Nikon has introduced the 300/2.8 VR in 2005, time when canon already had monopoly over the sports photography products, and continues to do until today.
General impressions I take from their history
While Canon was always more consumer oriented, making itself more accessible to the users, Nikon followed a strict tradition, making cameras for photographers and was never too concerned about launching the new "christmas gift camera for under ***$.
Canon made alot of daring experiments in technology and marketed itself as a way opener.
Canon took the digital era very seriously, developing the 1Ds - the professional full-frame digital camera from early development of the digital market (spring of 2003), while i feel that Nikon was still counting on film users when it did not launch any full-frame digital camera until late 2007. Not to mention that Canon's sports and journalism camera, the 1D (2001) had a crop factor of 1.3 instead of 1.5 like Nikon's D1.
Nikon developed many DX (1.5x crop factor) lenses; Canon made the EF-S mount, specific for the crop cameras, the EF-S lenses do not fit on full-frames or the 1D.
Why people choose one or the other?
There are numerous aspects which users might choose from when picking a brand, but most of the time the choice is made because of a previous experience, or in worst cases because "that guy has one". Buying yourself a certain type of camera because one particular photographer takes very nice photos with it is ridiculous.
In my case, i went with Canon because i bought my first camera (eos 350D/XT) when there were very few dSLR's in my market and even fewer second hand. Nikon was totally out of the question being rare and lenses and accessories being very scarse, and the more noob-friendly (at that time) Canon was at hand and the internet was filled with used lenses, new ones, adapters, accessories for it and the choice was quite easy for me. I don't regret it, because i've owned about 9 EF lenses and tried many more (28-70/3.5, 70-300/4.5, 28-135is, 50/1.8, tok.19-35, 24-70/2.8L, 70-200/2.8L, 85/1.8, 24/2.8) (tried 400/2.8 IS, 70-200/2.8is, 70-200/4is, 15fish, 16-35II, 17-40, 24-105, 50/1.0, sigma 8mm, and many manual lenses adapted).
I imagine people choose Canon because it seems more user-friendly, but i honestly like the color spectrum better in difficult light situations. In daylight and clouds, give me a Nikon d80 and i'll be happy, but anything interior with or without flash, i'll need a Canon to do the job, or a professional grade Nikon (d3, d2,d700).
But my next camera might be a Nikon because i've had reliability issues with my EOS 5D (who makes a camera out of plastic for 2700$? honestly... [i did actually buy it right before the 5DII came out and payed 1900$ new from amazon, but retail price is the previous one]) I dropped mine from a meter and it has a nasty crack, and it's a b***h sending it to the service specially since i don't have warranty anymore. Lenses also feel more flimsy than the Nikkor equivalents, though i can't really complain about the 70-200, the 24-70 had an awful design, and i absolutely hated it for it's sheer size and ugly look without a hood (which is also huge). That's why i now own a 24/2.8 and a 85/1.8 (great bang for the buck lens, nice shallow DoF, great for portraits, useful for full body shots). I might even do something as insane as buying the Sony A-900 if prices drop and they extend their lens variety soon.
What I look for in a camera
Firstly and most importantly: i can't imagine going back to crop sensor after having worked exclusively for more than a year with a 35mm sensor; a second and very important factor is how well the processor and the sensor translates images into digital colours. As i've said earlier, entry-level Nikon will be awful in an interior and especially where you meet 2 different types of light (e.g.: tungsten and fluorescent), i find most Canon cameras handle this problem better, and yes, the D300 is almost as bad, even in cloudy evening light - some long exposures have been impressive, but that is not a dealbreaker.
I still haven't tried the d700, but while taking a few sample shots with the D3 I was quite satisfied (though still ranting about the 5DII and it's very natural reproduction of colors - it might have been the lighting too, can't tell for sure until i have one for an extended period of time).
Breaking it down:
+better construction (bodies and lenses more resistant to weather and accidents)
+more buttons and easier to control layout (especially in the more advanced models like d300 d700 d3 d3x)
+incorporated wireless flash system for models above and including d80.
+good sharp zoom lenses
+pop-up flash for enthusiast full-frame camera (d700) [this is more useful than you think if your only camera is a slr. having virtually no fast and quality primes you will be sure to need this]
+old mount which assures that you can use old lenses, but since those have primitive coating, I would stick to more current models.
+high fps, af and fast response time in more advanced models (d200,d300,d700,d3,d3x)
+easier to shoot in lowlight because of the focus assist light
-annyoing focus assist light
-few megapixels in most cameras (and YES, they do matter if you have the right lenses)
-interior white balance difficulties with entry-level models.
-NO fast (under f/2.8 and/or sharp) wide primes (with few ridiculously expensive exceptions).
+more wide-spread and popular, lenses and deals are easier to find (over 50 mil lenses up to 2008, that will ensure a good s.h. market)
+wider selection of lenses
+mount very easy to use with many adapters thus making it possible to use a very large variety of manual focus lenses.
+good color reproduction indoors and when in many difficult shooting situations
+very fast primes (85/1.2, 35/1.4, 24/1.4, 50/1.2, 50/1.0 - if you have the money)
+high resolution sensors is a priority (this matters only if you have very good lenses).
-bad product control with lenses older than 2007 - unsharp wide-open
-old lenses on manual focus don't work on new bodies because of the 1987 mount change, original adapters are rare and cost as much as a professional lens.