They do typically sell for a premium over other EPDGs but the scarcity question versus other EPDGs is questionable. I personally think the Piedmont 350's are much tougher to find and their pricing reflects it.
However, the EPDG versions definitely get a premium.
I think the scarcity of elite 11 EPDGs might be answered better from this thread below. Logically if the EPDGs were printed before the Piedmont 350's then there would be a somewhat consistent amount of elite 11 EPDGs as other 150/350 or 350 only cards that are available with EPDG backs.
http://www.net54baseball.com/showthread.php?t=231030