I made this prediction on our coveted IRC channel earlier today, but the confirmation of Destiny PVP appearing at E3 has bolstered my mind powers.

I'm prediction that at PAX we'll have a playable PVP arena, with guardians locked at the level cap. We'll be able to choose from all 3 classes, with a separate characters for each different focus. We'll choose from two or three different arenas to battle with a handful of other players.

My guess is that we'll be seeing PVP at PAX as opposed to co-op or single player missions/strikes just because of the logistics of recycling and reusing leveled characters for four days. Level-capped guardians seems like the easiest way to do it, and PVP would probably be easier to implement as a standalone for their booth/kiosk/corner.