The short answer is that it depends.
Let's forget digital for the moment and just think about film as pixel densities just confuse the issue. To start with consider Peter's case. A given lens at a set subject distance will produce a given image height on the film regardless if the film was full frame 35mm (24mm height) or APC (15mm height). Assume the image height is 5mm and we want the image on the print to be 5cm the amount of enlargement will be x10. In this case the crop factor plays no part in the equation.
On the otherhand if the image was to fill the height of a full frame 35mm (24mm height) camera it would over fill the height of the APS-C (15mm height) frame because of the reduced field of view. Therefore using the same lens for a APS-C camera the same subject has to move further away to fit into the smaller field of view. This where the effective field of view of a 400mm lens becomes 640mm on a 1.6 crop factor camera. At this point Peter's statement is still true.
The problem starts when we come to printing the images.
The amount of enlargement required to produce an A4 print from the full frame 24mm high image is x8.75 compared to x14 for the APS-C 15mm high image. This is 60% extra enlargement which will show up camera shake problems more.
This extra enlargement also has an effect of Depth of Field Calculations and Bokeh. A reason why some prefer a full frame sensor to a APS-C sensor.
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