Too much sandbox in a game, and players are tossed into the world with too little direction and structure, not very fun or exciting for the average player.

Too quest driven, and while you get a more exciting and structured game, it'll be the same thing, every time you play through, and eventually players will want to do something aside from said quest, players will start yearning for the freedom to do what they wish.

I would suggest having quests available that coincide with players and player actions. IE, if you have a bunch of players who gang up and attack NPC and PC trade caravans, eventually NPC's will set bounties on them, and in the absence or supplementation of the bounties, on NPC raiders.
NPC's might be able to hint towards any area highly stocked with shiny bits that exists outside the city, especially if said location is a players stash! Though one would expect either excellent hiding of said bits, or defensive emplacements, such as robots, hired guards, or simple traps galore. (Alternatively, to give players a bit more incentive to stash their horde outside towns, either storage would be limited within, and or housing could be broken into. Though traps and the like still apply, albiet to a lesser degree so as not to be as much a possible threat to the town).
Players could eventually found a town themselves, or alternatively, burn it to the ground or subjugate it. Players could attack and raid cities, though it would be incredibly difficult to take and hold (Though potentially equally rewarding).
Basically, players, if they so choose to do whatever it is that makes them applicably for PvP, can be treated just like NPC's in terms of quest objectives.

Thoughts?

Due to the eve reference in the sandbox vs open world post, I thought it might have been denied, but it was just a really...really...long 3 or 4 day wait to get my topics posted, so disregard on this one.