P. S. Ray, as discussed many times over the years here at LuLa, there are inherent technical reasons backed by experimental data as to why one is likely to get likely to get less noise in a smaller format at a given EI (e.g ISO 200 in 4/3" format) than with a larger sensor at the higher EI used to get equal DOF and exposure time in a larger format (e.g. ISO 800 in 35mm format). In a nutshell: because in this particular scenario, there will be about the same photon count and amount of photon shot noise, but the larger sensor (and longer, wider signal paths and larger components in the analog signal processing path) will generate more electrical noise.
BJL,
Of course, there are usually many technical differences between all brands and sizes of cameras. Nobody buys a camera based on the consideration of just one factor, such as format size. (At least, I don't).
There is usually a huge range of technical and cost advantages, and disadvantages to consider, in relation to one's purpose, and usual photographic method and style.
For some folks, weight is a major consideration, and most people would be willing to sacrifice to some degree the potential quality and resolution of an image for the sake of the convenience of low weight. The question then becomes a matter of degree. 'How much is the weight saving, and how much is the image-quality loss?' A significant weight-saving with the consequences of an insignificant or less significant loss of image quality, would probably appeal to most people, provided there was no major increase in price.
However, as you know, I'm a great fan of the scientific method. When considering the effects of just one factor, such as format size, one needs to keep all other factors the same, if possible, otherwise the effects of that one factor become confused with the other factors.
So, to get back to my main point, if the pixel size and quality is the same for both formats, after all the in-camera processing of the signal is complete, as it is comparing the Nikon D7000 with the Nikon D800, (according to DXOMark) then the larger format has all the advantages and no disadvantages.
The larger format then becomes 'effectively' cheaper, lighter, and, over all, produces better image quality (and no less than equal image quality, at a minimum, in certain circumstances when the larger format is cropped to the same size as the smaller format).
Now, if you escape from the scientific method, and include all sorts of other factors not directly related to format size, and exclude certain disadvantages of the smaller format in terms of the general lack of flexibility of the focal lengths of whatever lenses are used, then you might as well stick with your iPhone camera.
To repeat, a D7000 with 50mm/F1.4 prime, might be lighter and cheaper than a D800 with the same 50mm prime but is not capable of capturing the same subject matter from the same position. If you don't have the time to move further back, or as is often the case, don't have the physical possibility of moving back, then you've lost the shot.
To give the smaller format that capability, you'd need a very high quality, and very expensive 33-50mm/F1.4 zoom. At 50mm, the quality of the images from both cameras would be the same (provided the zoom lens was of equal quality to the 50mm prime). However, at 33 mm on the D7000 the image quality would be worse (in terms of resolution and noise), although the angle of view would be the same as that from the 50mm prime on the D800. But at least you would not have missed the shot.
The extra weight and cost of a 33-50mm/F1.4 zoom lens would make the D7000 at least as expensive and at least as heavy as the D800 with 50mm prime. Okay?