I think that the reason that it is called Premium Economy is so that travellers can adhere to corporate policies limiting travel to economy.
Definitely. Business requires approval from a manager higher up the line and more justification from me. PE is much easier. On QF a few years ago when I did it PE was the back of the A380 on the top deck and the main advantage was larger seats and not being able to reach the seat in front of you when you straightened out your arm. Last trip a few weeks back I was in economy on an A380 and it seems the back of the top deck was also economy, then PE, then business moving forward.