I think in the ideal MMO a limited amount of players should be able to become "heroes", seeking to keep their status (becomes it has advantages), and others should try to acheive it. It's what EvE online does extremely well : players are all racing against each other to become the king of the hill, the bandit warlord, the corporation manager, the head of the security forces, and so on. What is especially interesting is that players are very far from just fighting each other over the actual ingame combat. They start social influence games inside corporations, try to take over political structures etc. That's the kind of (slightly emergent) competition I want to see in a truly pvp MMO.
Edit : let's expand a bit :
First, the gameplay itself should require more player-player interactions, and not necessarily competitive or cooperative. The classical problem with this is that it's very difficult to have meaningful interactions with people you don't already know outside the game, without devoting waaaay too much time to the game. Even a casual player without friends playing the same game should be able to play with others, and that I think is a real challenge in game design.
Secondly, in most classical MMO's, when you have seen/defeated everything that the game had to offer, that's pretty much it. You can still play for pixel crack, sure. But that's empty. The end game shouldn't be a competition over nothing like a CS game, but it shouldn't be a quest for super rare pixel crack either. I think end game players should, depending on what path they chose, be more like guild masters, organising their alliance, training other players, etc. and generally monopolizing the benefits of your guild. But also fight against the inside threats, especially people from the same organisation as you trying to take command.
The original Ultima Online was a great example of a sandbox online RPG. Everyone was a role, whether it was something they chose to be or something thrust onto them while they played. The way the roles interacted together made for some awesome on the spot (dynamic) gameplay. Everything you did could impact another player. You had murderers, thieves, adventurers, traders, miners, crafters. People even created their own little niches for making money, like house decorating. It was a true RPG, but it simply had other players instead of NPC's. The key with these games is giving players choices, with lasting consequences that impact the world and other players. You never get to play the bad guy in modern MMO's, and no being Sith or something with thousands of allies around that you can't attack is not being a bad guy in this sense. Everyone plays the same role really in a world that seems to revolve around the player character. Its not very immersive for me when I feel like i'm playing single player with my own story, with others doing the same thing or are also supposed to be the same hero.
Eve Online does a good job at sandbox style. Just for me I don't really like that style of gameplay of rock/paper/scissors or money invested having such a large impact in pvp. Its a good team game though but can feature hours and hours of nothing happening
Darkfall has decent pvp and allows you to be the bad guy, but really thats all it has. You only get bad guys in that with no sense of wider community or people with different agendas. Its just kill kill kill with no real point to it. As a pvp style sandbox game its decent (just kind of died out through several issues). Darkfall 2.0 is out next month so worth a try
I would really like to see a true sandbox game that doesn't hold you hand thats released by a big name company, that allows players to take each other's metaphorical candy. All you need is game design that allows players to hunt down the bad guys, you shouldn't just remove them from the game. It adds a whole other dimension,engages the player and gets them invested in what they're doing, like theres actually something on the line when you have some consequences.
Risk vs reward, player choice and consequences, design that appeals to a broad playerbase (not just pk's), player skill based pvp and as little hand holding as possible, thats what i'm looking for in an MMO.
