Facial distortion is evident when features like nose size and ear size are perceived as incorrect. Our view of what we look like is derived from our dressing mirror. If the photographer can replicate this mind’s eye view, facial distortion becomes moot. In most cases, if the photograph just stepped back, the problem is vanished.
OK a more scientific approach. Every image has a “correct” viewing distance associated with it. If the image is viewed from such a distance, most all problems related to perspective distortion are moot. Fortunately, most pictures are immune from perspective distortion so any viewing distance is OK. The human face is a major exception.
What comprises the correct viewing distance? This distance intertwines focal length and the magnification applied to make the final display. Suppose we make 8 by 12 inch print or display same on a monitor / TV with the same dimensions. A full frame 24 x 36mm must the enlarged 8 ½ X to obtain this size. A compact digital frame is 16 X 24mm and we must enlarge 12 ¾ X to get to the same size.
From a scientific point of view, we should use a lens with a focal length of about 2.5X normal when doing portraiture. OK to round most of the values. At this point let me add that in art, there are no rules so you are free to follow your heart. For the FX that’s about 105mm focal length. For the DX that’s 75mm. These values are approximately the corner to corner measurement of the frame size time 2.5.
The correct viewing distance minimizing distortion is focal length multiplied by magnification. We observe an image 8x12 inch shot on FX with 105mm enlarged 8.5x. The viewing distance is 105 X 8.5 = 890mm = 35 inches.
Using this same formula for a DX with a 70mm making a 8x12 display, the focal length is 75mm X 12.75 = 950mm = 37 inches.
My conclusion -- the FX with a 105 will display about the same degree of facial distortion as the DX with a 75mm mounted.
“My question is: will a photo taken with a 28mm focal length on an APS-C sensor look identical to a photo taken with a 40mm (28mm equivalent on a full frame sensor) on a full frame sensor?”
Answer DX 28mm X 12.75 = 350mm = 13.7 inch viewing distance.
FX 40mm X 8.5 = 340mm = 14 inch viewing distance.
Conclusion – They will look about the same.