I imagine the question may have come up somewhere before, but considering it wasn't in the answered questions bit, I suppose a little more debate about the concept wouldn't be a terrible idea.
That being said:

Both design types in the extreme are usually lacking severely in certain aspects. Too sandbox and the average player has no idea what to do, no structure. In EvE, for example, to have any sort of significant effect on the game space one must become the leader or influential member of a massive player corporation. Anything else, and you're pretty much inconsequential. A nobody.
Alternatively, quest driven storylines can make you feel like a hero(Or villain) al-la city of heroes, but with a distinct lack of polish in other areas (Such as PVP) and virtually nothing else to do aside from missions, no matter how entertaining they are, the fourth or fifth time through it gets rather monotonous.

My concept...
Like most things in life, balance is needed to keep it healthy. Imho, various "cities" (Ie, large settlements) with vendors, bounty hunters, tinkerers, survivalists, etc with appropriate tasks that can be given to give a player some currency and XP. Out in the wilderness however, lies the true heart of the game.
Essentially, from what I've garnered thus far, mankind is once again in a sort of frontier age, with a few bastions of "Civilization" but the vast majority striking out into the world for fame and fortune. Unlike the unspoiled nations during said period however, fallout has plenty of inhabited ruins, renegade robot controlled facilities, and hostile wildlife infested caves and such with plenty of weapons and loot to be had. So a bit of goldrush/treasure hunt/colonization.

Players may be given a tip (With a finders fee) from an NPC, giving them a ruin to loot, or perhaps the location of some roaming bandits that have been causing trouble, or some lost tech or legendary proportions. The twist being that the supposed ruin just happens to be home to a player or group of players, the bandits/raiders are in fact a group of hardcoe pvpers who regularly raid caravans and smaller towns, and you're not the only one after said legendary tech.

Some kind of system that allows players to eventually found their own towns, and other still to burn them down to the ground, or subjugate them. For some to take slaves, while others to free them. Enclave and super mutant attacks, along with NPC raiders on towns and cities, or mercenary/assassin contracts on players of note, both from NPC enemies and available to certain players.
Obviously borrowing some elements of eve here, but preferably without all the damned clicking and waiting around.

Ultimately, player driven, quest supported. Sandbox mostly, with roaming NPC elements to mix things up, as well as attacks to fend off and towns to raise. Preferably without a typical leveling system, in so that a group of newbies could feasibly take on a veteran, though the veteran would have an obvious advantage.

Well, that's the gist of my ideas on FOOL being sandbox or quest based....and quite a bit of then some XD

Good ideas, i like the part about building settlements. If that does happen, there should be a time when npc's start to migrate there. Also, if one person starts killing npc's, do they respawn eventually? I put the 'Skill' in 'Kill.'
Wait, what?

Completely want a Overall story line AND the choice of sand box play. That's the big difficulty. How to implement all this.
There is the problem of player structures. How to do it without interfering with the devs design decisions and nipping the inevitable exploits that will be found in the bud.
How to let guilds have an effect on the world without making them so powerful that they can dominate a server so nobody will want to be in that server. While at the same time letting players feel as if they can change the world around them given enough work.
Find the balance and this will be epic. MMO's... MMO's never change...

So you want colonization and growth of NPC's eh?

Shameless plug

http://gamesas.com/forums/viewtopic.php?f=7&t=7271

Depends if their going multi server (Aka WoW style) or Single shard (Aka EVE style)

If they go WoW style they can just put servers with bare minimum NPC's and let players have a go while phasing out NPC's slowly. If players want heavy NPC interaction, np, they have a server for that.

If it's EVE style and everyone in a single world (my god please!) they can have the NPC 'nation/factions' that have their own (very large) territory that can be upgraded, but not expanded, while the 'zones/wastes' can be controlled by player nations.

This would be a 'mega server' but there wouldn't be 40x copies of the same game where people all have different experiences in the same town, at the same time. Thing is politics can get crazy, players can form hatreds but at the same time you have this ready made printing machine of events that just goes without any dev having to touch it.

Depends if their going multi server (Aka WoW style) or Single shard (Aka EVE style)

If they go WoW style they can just put servers with bare minimum NPC's and let players have a go while phasing out NPC's slowly. If players want heavy NPC interaction, np, they have a server for that.

If it's EVE style and everyone in a single world (my god please!) they can have the NPC 'nation/factions' that have their own (very large) territory that can be upgraded, but not expanded, while the 'zones/wastes' can be controlled by player nations.

This would be a 'mega server' but there wouldn't be 40x copies of the same game where people all have different experiences in the same town, at the same time. Thing is politics can get crazy, players can form hatreds but at the same time you have this ready made printing machine of events that just goes without any dev having to touch it.

Personally methinks the only way to really have it done proper is a single large server, a huge wasteland with relatively little in it in player controllable areas (Aside from a few choice locations that would be easier to build upon to make a base, both ruins and natural locations) with the fringes being EXTREMELY dangerous but very rewarding as well. Intense radiation and intensely irradiated creatures.
The thing is, players would have to hold their towns/bases against not only players, but NPC's as well. To answer MadSun's question (NPC's respawning) I would say they aught to, but not in the typical sense of a guy dieing and reappearing 5 feet away.
Wanderers, mutants, raiders, rogue robots, etc aught to spawn from specific hubs or the fringes of the map and wander around or head to a specific location. IE, if there is a massive raider camp out in the middle of BFE, raiders will spawn from inside the facility and wander out from there, until it is taken over or destroyed, in which case raiders will spawn on the fringes and eventually attempt to construct another camp from which raiders can spawn.

There will only be X amount of spawn points existing at any given time (Camps, caves[for critters[ ETC) and when one is destroyed, the effected NPC type will attempt to find/create a new one. With the exception of super mutants, who will aggressively expand and have no set limit to the camps, and possibly raiders or enclave.
This gives the land a constantly changing landscape as bases are destroyed or flushed out, and enemies are forced to create new territories of their own.

Ok, I have seen alot of excellent ideas, things I would love to see on V13 myself, as a longstanding fallout superfan. One thing I myself want to see is named NCP permanent death. If player Ace kills the NPC raider king Varius, then Varius needs to stay dead and player Gott should not be able to come by a few days later and fight the same guy.