Ever since the crop factor sensors came out it seems like peeps have been trying to find magic where none exists. Here's a short list of the nonsense that I've seen around the web. Please tell me if I'm out to lunch on any of it...
1) Crop factor sensors give more depth of field: This one is usually the result of trying to make the subject look the same size on both a crop factor sensor and full frame, so the full frame image is shot at a higher magnification. Magnification goes up, depth goes down when the aperture doesn't change. Or the full frame camera is moved closer to the subject to get the same apparent subject size and as the camera gets closer the magnification increase. Again mag goes up, depth goes down. Here's a simple test between a full frame sensor and a crop factor one. Notice how the depth doesn't change.
2) Crop factor sensors give you more magnification: This one should be common sense, but people think that because the subject looks larger on screen or in print with a crop sensor they assume that the image is magnified. But it's not, it's simply an enlargement and no different than cropping an image in post. Terms like "screen magnification" and "print magnification" don't help.
3) Crop factor sensors change the ISO because there is less surface area on a crop factor sensor: You can't think of sensor in terms of total surface area, because a digital sensor isn't a single light sensing device (like a solar cell), they are made of millions of light sensitive photo receptors (pixels). All the pixels on a full frame and a crop factor sensor get the same amount of light from the lens, and the intensity of the light that's projected by the lens onto the sensor doesn't change.
Here's my .02:
Canon's 5DS has a 50MP sensor, and if you were to take a shot with it and crop it down to a 1.6x APS-C crop factor you'd end up with roughly an 18MP image. So what would be the difference in the depth of field, ISO, resolution, or any other basic characteristic if you:
A. Cropped in post to that 1.6x?
B. Taped off the outside of the sensor so that it's now APS-C sized?
C. Canon making an APS-C sized sensor with the same physical characteristics as the taped off full frame sensor in B above?
The answer is nothing. The depth of field, ISO, aperture, etc. wouldn't change. The amount of light striking the sensor at a given aperture doesn't change. Would the subject look larger in the frame? Sure. But that's just an enlargement.
If there are any differences between a full frame and a crop factor camera then those differences are due to the way the chips are physically designed (pixel size, pixel density, etc.) and not the fact that one is physically smaller than the other. So cropping the image circle with the sensor and cropping in post are the same.
So where am I wrong?