I've seen Trex (and other fake woods) on decks, and have been greatly underwhelmed. The appearance isn't very good, they fade (they all claim they don't, but they all do, very significantly and very quickly), and some (I forget if Trex is one) are prone to warpage. And their cost, when compared with pine or even cedar, are exhorbitant.
If you already have a natural wood deck, I recommend sticking with a natural wood pergola. Anything else won't look right. Doesn't even need to be the same wood, particularly if it's free-standing.