Personally, I'd like 'open' to be actual MMO-side, with 'solo' play mode being just that, solo play, your own universe where you can single-player to your hearts content.
But then again, I'd like 'open' to have actual player-driven economy, persistent player-driven things happening, groups and alliances claiming territory and resources...
These may not be goals of the Dev Team, which is okay by me, just a bit disappointing from the perspective of what this game could be.
Perhaps eventually they'll introduce a Persistent World Server or something, a place for more complex play and player-to-player interaction. Or maybe some day they'll abandon the product and release the server code, and we'll be able to mod it into that.
However, I'm willing to wait and see, things like that take time and effort, and Frontier is working hard on just getting the Core game launched.
EDIT: As for why I'd like to have a world with PVP and other sort of player-to-player interaction:
I love emergent systems. I love emergent gameplay. And I dearly, dearly love playing with, and against, other players.
When those players also voluntarily want to play with or against me.
I do not want Solo-Play to be an unviable playmode. I want it to be an option. I don't think I want to play it for long. I certainly don't want Solo-play to impact online 'open' player economy because then it's simply PVP with another name, from players who can't be challenged directly. Personally, I think a valid way would be to create a working player economy, then 'shadow' it to Solo, so that transactions in Solo Play mirror 'Open' only one way.
I also like building things. Building grand things with other people, and building small things with just my own effort in-game. Once they are built, I want others to come and see them, use them, try to break them or take them. It keeps the game interesting.
I love the idea of taking a group of players 70 000 ly from starting area, setting up a refinery and factory, mining and slowly creating a place for our colonists to grow into inhabited worlds, building our own ships and guns and missiles, our own stations and outposts, eventually perhaps to find the 'empire' or 'federation' expanding to our doorstep... And beyond.
In short: I want online 'Open' play to be a viable long-term play mode, with a magnitude more goals than there are available right now. Not in the way of 'content', that simply spoon-feeds you 'do this and you'll have shiniest trinket', but in the way of 'these things are possible for you, if you can manage it'.