I had a Nikon DSLR and my father in law bought a canon. He was so impressed with the pictures from my Nikon he ditched the canon and went Nikon. His pictures were still cr*p. Turns out he wasn't a very good photographer
Both Nikon and Canon have their strengths and weaknesses. In the P&S / compact market, Canon
is better, while in the DSLR market, Nikon. Therefore, it can't be generally stated
"Nikon is superior to Canon" - again, Canon P&S / compact cameras
are better, particularly now that they have announced the
G1X Mk II, against which only the rumored Nikon P800 could have any chance in the same (large-sensor compact with non-interchangeable lens).
DSLR-wise, assuming starting from zero (without previous investment in either system, lens-wise) on the other hand, I personally would go for Nikon because of the superior sensor tech. Canon has certainly been lagging in that dept for 2-3 years. The Sony sensors used by Nikon DSLR's are certainly better than Canon's own sensors.
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The result that he showed was that great photography starts with the person behind the camera, not the camera.
Nevertheless, a large-sensor camera will always perform better in challenging lighting (low light, large differences in lights requiring a sensor with large DR etc.) Small-sensor cameras, incl. the iPhone, will always have the handicap of high noise and low DR, even if their lens and, WRT iOS, their WB algorithm are otherwise excellent.
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EDIT: One thing that I have noticed, and I'm not talking after doing extensive research, but just watching people at concerts, the iPhone camera (sucks) is less optimal at a concert venue... I have gotten some incredible shots at concerts, but the quality for the vast majority has been tragically sub-par. Someone told me about a concert goer being confronted by security at a concert for taking pictures, and after seeing it was an iPhone, the security guard let the guy alone saying 'I can't throw you out for using an iPhone to take pictures here, they aren't going to be any good anyway.' It's probably internet lore by a 'Droid fanboy, but I have tons of blurry and overexposed pictures to remind me of concerts I've been to. *SHRUG*
Of course you can't make good handheld low-light shots with an iPhone. It painfully lacks any kind of image stabilization, meaning it'll always try to shoot at 1/15s (extendable to 1/20s on the iPhone 5/5c and 1/30s on the 5s using AppStore apps like 645 Pro - see my dedicated report
HERE), which will almost always mean motion / camera blur, particularly in a concert where both the subjects and the camera moves. And, unlike top cameraphones like the Nokia 1020, there isn't any kind of OIS in the iPhone, meaning there is simply no way of getting rid of camera shake, unless you can find a way to stabilize the phone. Which is pretty much impossible in a concert.
And you can't shoot at, say, 1/100s to reduce motion (with some very high ISO) because iOS doesn't allow for configuring the shutter speed / ISO. In this regard, it's vastly inferior to all other smartphone OS'es.