The simple answer is you can shoot a great portrait with a crop or full frame body. If I had all my equipment with me, I would pick my 6D and 70-200mm f/2.8 IS II, with the focal length dependent where I was. Indoors I would likely be closer, but outdoors I might want considerable distance between the background, the subject and the camera. (10-15 feet camera to subject, for example.)
If you like a paper-thin depth of field, then maybe you would shoot an f/1.2 lens or f/2.0 lens wide open, but that would not be my personal choice. Lets say the head is at a 15 degree angle from straight on. You likely cannot get both eyes tack sharp wide open, and the ears could be a total blur. If that is to you liking, so be it, as this approach is in vogue right now.
I posted a portrait example on another discussion about the 85mm f/1.2 where I am in the minority on wanting a reasonable depth of field. On the other hand, you can resolve individual strands of hair on a 10 megapixel sensor using a 40D, 70-200mm f/2.8 IS II at f/5. The background is totally blown out, the eyes, teeth are very sharp, and the ears are just nicely of the the depth of field, but not blurry.
It is more a case of what camera and lens is in your hand when a portrait opportunity comes up. Then you adjust your distance and f-stop to produce the type of image you prefer.