I think the difference in quality due to cropping is not the real issue here. I think the differences encountered in the portrait setup are moot compared to the real issue which is facial distortion.
The camera doesn’t perceive things exactly the same as the human visual experience. That being the case, we must hone our skills to make portraits with the camera that please our clients. The portrait subject has a preconceived notion regarding their self-image. This is their view of themselves as seen in the dressing mirror. As a general rule, our task is to duplicate that view. If you succeed, you will have satisfied clients.
We are talking about “perspective”. Things close to the camera reproduce large and things further from the camera reproduce small. If the camera is positioned too close to the subject, the nose reproduces too large and the ears too small. The remedy is simply step back. Increased distance, camera to subject is the key. As we step back, the ratio of the distance between camera and nose and camera to ears diminishes. In other words, as we step back, we minimize facial distortion.
Stepping back is easier said than done. Sometimes the studio (workplace) is too tiny to allow the necessary increase as to subject distance. Thus we are forced to work in close, and this distorts facial features. Sometimes we use a lens with too short a focal length. When we do, the natural tendency is to compose by filling the frame in the viewfinder. If we just would step back, everything would be OK, but we abhor the empty space around the principal subject, so we stay put. The results are aggravated facial distortions.
Medium telephoto to the rescue: If we mount a moderate telephoto, we are forced to step back. This action is the ticket. The question becomes, “what is a moderate telephoto”? Over the years, portrait photographers gravitate to a focal length that is about 2X thru 2.5X longer than “normal”. So the questions become what is the “normal” focal length for my camera? The accepted normal for the FX (full frame) is 50mm. Thus the portrait focal length range is 100mm thru 125. For the DX (compact digital) “normal” is 30mm. Thus for the DX, the portrait range is 60mm thru 80mm.
We are talking rule of thumb; art has no norms so you are free to follow your heart. As to what is “normal” for the camera lens. The industry views “normal” as a focal length about equal to the corner to corner (diagonal) measure of the film or digital format. You will need to check your camera’s specifications to find the dimensions of the frame. As an example, the FX measures 24mm wide by 36mm long, the diagonal measures about 44mm. The DX measures 16mm wide by 24mm long, the diagonal measure is 30mm. If we mount a “normal” focal length lens, the angle of view is about 45° with the camera held horizontal (landscape).