Re: Advantage of APS-C over full frame in quality?

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Wouldn't the image from a full frame digital camera with a 300mm lens cropped to the area captured by an APS-C camera (with the same lens and distance) be equal to the quality of the image captured by the APS-C camera? 
 
I would say yes and the only advantage of the APS-C would be its lighter weight and price.
 
The Wikipedia says no
 
From Wikipedia: Comparing full frame to APS-C

For example, a 200 mm lens on a camera with a crop factor of 1.5 has the same angle of view as a 300 mm lens on a full-frame camera. The extra "reach", for a given number of pixels, can be helpful in specific areas of photography such as wildlife or sports.<SUP id=cite_ref-5 class=reference>
[6].

^ Barbara Gerlach (2007). Digital Nature Photography: The Art and the Science. Focal Press. p. 67.
ISBN 9780240808567. http://books.google.com/books?id=iNrWzL_NpWkC&pg=PA67&dq=%22reach%22+crop-factor&lr=&as_brr=0&ei=6Yc2So6ZDpDSkwSy9JmdBQ&hl=en&e=v1

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