There can definitely be some benefit to be gained by using a crop sensor camera when longer focal length is desireable. It is one of the reasons compact "superzoom" cameras can give fields of view equivalent to 1000mm+ focal lengths on a full frame camera with a much smaller lens than would be required to get that same FoV using a full frame sensor camera.

If the pixel density is the same on a FF camera and an APS-C camera, then there would be little to no benefit (all other things being equal). But the pixel density is rarely the same. A typical APS-C camera might have a 20MP sensor that gives a pixel spacing of about 4 microns. A 22MP FF camera has a pixel spacing of 6.25 microns.

The crop factor of a particular sensor is based on linear measurements, but pixel density is measured in terms of pixels per area. This means the number of pixels on a FF sensor that fall within the space covered by a 1.5X APS-C sensor is not 1/1.5X, but 1/2.25X of the total number of pixels on the FF sensor. In the case of our typical 22MP FF camera, if we crop the image by 1.5X in the linear measurements we are only left with a pixel count of just under 10MP. In the case of a 1.6X APS-C sensor it would only be about 8.6MP.

If 8-10MP is sufficient for your intended display size, then there will be very little difference between cropping the FF image or using the APS-C camera (all other things being equal). But if you need more than 8-10MP resolution for your intended display size, then the advantage of the APS-C body becomes obvious.

If you magnify the image projected by the lens, such as is the case with a teleconverter, you spread the light thinner and give up aperture in terms of the f-number used to calculate exposure. But if you increase magnification when printing or displaying the image you don't lose any aperture in terms of exposure. You do, however, lose performance in terms of perceived image noise when you magnify an image. Displaying the same image at different viewing sizes (magnifications) also affects the depth of field as perceived by the viewer at the same viewing distance.

Beyond the relative pixel densities, there is also the issue of comparing different generations of technology. A newer FF body might do better cropped to APS-C magnification compared to an older APS-C body. On the other hand, a newer APS-C body may do better when compared to a cropped image from an older FF body.

Also please note that when you crop a FF image to the same magnification as an APS-C sized image, you have just thrown away the extra light that the FF sensor collected to give it that one stop advantage in terms of noise.

There can definitely be some benefit to be gained by using a crop sensor camera when longer focal length is desireable. It is one of the reasons compact "superzoom" cameras can give fields of view equivalent to 1000mm+ focal lengths on a full frame camera with a much smaller lens than would be required to get that same FoV using a full frame sensor camera.

If the pixel density is the same on a FF camera and an APS-C camera, then there would be little to no benefit (all other things being equal). But the pixel density is rarely the same. A typical APS-C camera might have a 20MP sensor that gives a pixel spacing of about 4 microns. A 22MP FF camera has a pixel spacing of 6.25 microns.

The crop factor of a particular sensor is based on linear measurements, but pixel density is measured in terms of pixels per area. This means the number of pixels on a FF sensor that fall within the space covered by a 1.5X APS-C sensor is not 1/1.5X, but 1/2.25X of the total number of pixels on the FF sensor. In the case of our typical 22MP FF camera, if we crop the image by 1.5X in the linear measurements we are only left with a pixel count of just under 10MP. In the case of cropping to match a 1.6X APS-C sensor it would only be about 8.6MP.

If 8-10MP is sufficient for your intended display size, then there will be very little difference between cropping the FF image or using the APS-C camera (all other things being equal). But if you need more than 8-10MP resolution for your intended display size, then the advantage of the APS-C body becomes obvious.

If you magnify the image projected by the lens, such as is the case with a teleconverter, you spread the light thinner and give up aperture in terms of the f-number used to calculate exposure. But if you increase magnification when printing or displaying the image you don't lose any aperture in terms of exposure. You do, however, lose performance in terms of perceived image noise when you magnify an image. Displaying the same image at different viewing sizes (magnifications) also affects the depth of field as perceived by the viewer at the same viewing distance.

Beyond the relative pixel densities, there is also the issue of comparing different generations of technology. A newer FF body might do better cropped to APS-C magnification compared to an older APS-C body. On the other hand, a newer APS-C body may do better when compared to a cropped image from an older FF body.

Also please note that when you crop a FF image to the same magnification as an APS-C sized image, you have just thrown away the extra light that the FF sensor collected to give it that one stop advantage in terms of noise.

There is definitely some benefit to be gained by using a crop sensor camera when longer focal length is desireable. It is one of the reasons compact "superzoom" cameras can give fields of view equivalent to 1000mm+ focal lengths on a full frame camera with a much smaller lens than would be required to get that same FoV using a full frame sensor camera.

If the pixel density is the same on a FF camera and an APS-C camera, then there would be little to no benefit. But the pixel density is rarely the same. A typical APS-C camera might have a 20MP sensor that gives a pixel spacing of about 4 microns. A 22MP FF camera has a pixel spacing of 6.25 microns.

The crop factor of a particular sensor is based on linear measurements, but pixel density is measured in terms of pixels per area. This means the number of pixels on a FF sensor that fall within the space covered by a 1.5X APS-C sensor is not 1/1.5X, but 1/2.25X of the total number of pixels on the sensor. In the case of our typical 22MP FF camera, if we crop the image by 1.5X in the linear measurements we are only left with a pixel count of just under 10MP. In the case of a 1.6X APS-C sensor it would only be about 8.6MP.

If you magnify the image projected by the lens, such as is the case with a teleconverter, you spread the light thinner and give up aperture in terms of the f-number. But if you increase magnification when printing or displaying the image you don't lose any aperture in terms of exposure

There can definitely be some benefit to be gained by using a crop sensor camera when longer focal length is desireable. It is one of the reasons compact "superzoom" cameras can give fields of view equivalent to 1000mm+ focal lengths on a full frame camera with a much smaller lens than would be required to get that same FoV using a full frame sensor camera.

If the pixel density is the same on a FF camera and an APS-C camera, then there would be little to no benefit (all other things being equal). But the pixel density is rarely the same. A typical APS-C camera might have a 20MP sensor that gives a pixel spacing of about 4 microns. A 22MP FF camera has a pixel spacing of 6.25 microns.

The crop factor of a particular sensor is based on linear measurements, but pixel density is measured in terms of pixels per area. This means the number of pixels on a FF sensor that fall within the space covered by a 1.5X APS-C sensor is not 1/1.5X, but 1/2.25X of the total number of pixels on the FF sensor. In the case of our typical 22MP FF camera, if we crop the image by 1.5X in the linear measurements we are only left with a pixel count of just under 10MP. In the case of a 1.6X APS-C sensor it would only be about 8.6MP.

If 8-10MP is sufficient for your intended display size, then there will be very little difference between cropping the FF image or using the APS-C camera (all other things being equal). But if you need more than 8-10MP resolution for your intended display size, then the advantage of the APS-C body becomes obvious.

If you magnify the image projected by the lens, such as is the case with a teleconverter, you spread the light thinner and give up aperture in terms of the f-number used to calculate exposure. But if you increase magnification when printing or displaying the image you don't lose any aperture in terms of exposure. You do, however, lose performance in terms of perceived image noise when you magnify an image. Displaying the same image at different viewing sizes (magnifications) also affects the depth of field as perceived by the viewer at the same viewing distance.

Beyond the relative pixel densities, there is also the issue of comparing different generations of technology. A newer FF body might do better cropped to APS-C magnification compared to an older APS-C body. On the other hand, a newer APS-C body may do better when compared to a cropped image from an older FF body.

Also please note that when you crop a FF image to the same magnification as an APS-C sized image, you have just thrown away the extra light that the FF sensor collected to give it that one stop advantage in terms of noise.