OK, the more detailed explanation. Sounds like it is needed.
Lets consider removing one variable to using a singe lens on both the cropped sensor (CS) and full frame (FF) cameras. Let's say the lens produces X lp/mm resolution in the center of the frame at some aperture we'll use. First lets make photographs with both the FF and CS cameras using that lens with the same settings on both.
Indeed, the lp/mm resolution is the same on both in the center. However, that level of resolution may resolve more detail in the final photograph on the FF camera. Why? An area - let's go with one millimeter - on the FF camera comprises a smaller portion of the overall frame than on the CS camera. One way of thinking of this is to say that "there are more millimeters to hold line pairs on the system with the larger sensor."
Point: At equal lp/mm resolution, the camera/lens system with the larger sensor can resolve more line pairs across the width (or height) of the photograph.
What about corners? Let's take this in two stages.
First let's look at a point that a distance from the center of the frame that would put it in the far corners of the CS sensor image. This will be the same distance from the center on the FF system - but, of course, that will be short of the corner on the larger sensor system. At the corners of an APS-C size rectangle, whether that rectangle comprises the whole of the CS image, or a portion of the FF image, the lens will produce the same lp/mm resolution. However, here as in the case of the center comparison, the FF system will be producing higher
system resolution at this point for the same reasons - an area at this distance from the center of the FF system comprises a smaller percentage of the full frame than on the CS system. Again, more millimeters to hold line pairs.
Second, what happens to the FF image
beyond the point that is a distance from the center of the frame equivalent to the corners of the APS-C sensor area? It will deteriorate - some or a little - but it remains
better than the CS system resolution for at least
some distance beyond the edges of an APS-C size rectangle. To be clear, the overall image produced on the FF system is capable of producing higher system resolution past the edges of this area. What are the possibilities here?
1. At a very large aperture on a very poor lens it is
possible that the image quality might decline far enough to equal or even be worse than that of the APS-C system resolution in the corners of the image from the smaller sensor.
2. On this lens at other apertures or on many lenses at any aperture, the system resolution of the FF camera might merely diminish only to that equal to what is found in the corners of the CS system.
3. With a decently good lens - the sort used by virtually anyone who cares about this stuff - the system resolution in the corners of the FF camera will likely still be higher than that on the CS system, especially when shooting at smaller apertures.
Of these three, what is the most likely scenario? There was a time when I believed the "common wisdom" about corner performance, which is based on lp/mm data from the corners of both systems. However, these ideas ignore the fact that larger sensor (or film) systems inherently
start with higher center resolution and ignore the fact that lp/mm resolution is irrelevant for this comparison and that lp/picture width or similar should be used.
I discovered that, precisely contrary to what people (often in forums like this one) continue to repeat uncritically, in many if not most cases, the corner performance as seen in
photographs made with the FF systems will be at least as good and often better than that on CS systems. Feel free to test for yourself.
I will note that vignetting (corner light fall off) can be more pronounced on FF systems with some lenses, and there is not positive compensating effect from the larger sensor. Fortunately, on most lenses this isn't even an issue, some people find some vignetting pleasing, and those who don't can easily correct this in post.
Dan
....as well as better bokeh effect on FF. FF also require optically sound optics or else it will amplify the flaws esp on the edges.
APS-C requires better optics than FF to resolve the same detail at the same DOF, because the photo is being enlarged 1.6x more for the same display size.
Im taking about sharpness consistency across the image edge to edge my friend. Get a bad copy 16-35 mkII on both cameras, same image, same settings, then ul understand what I mean. The FF Edges will be mush and the crop sensor will use more of the 'sweet spot'
APS-c has longer focal length advantages...
This is due to the pixel density of the sensor, not the size of the sensor.
You are right but I havent given a scietific response why are you? Lol,
...but that dosent translate into higher IQ, FF easily wins there.
Not always. If the APS-C sensor is more efficient, has more pixels, has a lens more than 1.6x as sharp, or if FF is focal length or magificantion limited, then APS-C can have the upper hand in terms of IQ.
No scientific reasoning is gonna prove to me that my 7d can give better IQ than a 1dx.
--
---
G Dan Mitchell - SF Bay Area, California, USA
Blog & Gallery:
http://www.gdanmitchell.com/
Google Plus:
https://plus.google.com/u/0/102554407414282880001/
Facebook:
http://www.facebook.com/gdanmitchellphotography
Flickr:
http://www.flickr.com/photos/gdanmitchell/
Twitter:
http://twitter.com/gdanmitchell 
