Does a hand pair beat a normal pair in poker?

The question is does a pocket pair (hold'em) or paired hole cards (stud) have more value than another pair, such as one made from community cards, open cards, wildcards or otherwise.

The answer is no. In no game does the location or state of the card (hole or open) have any influence on the value of the final hand. A pair is a pair regardless of from which cards it is formed.