I actually think I'd like the former idea, setting the PC loose into the wasteland to choose what you want to do without any universe-altering civilization-ending Grand Quest to distract you.
That's what makes me wonder if a Fallout MMO would work. So much of what we enjoy in Fallout has nothing to do with the main single-player storyline. It's exploring, and fighting, and crafting and (now) settlement building. I wonder how that would work in an MMO, though. Star Wars Galaxies (SWG) back in the day before the New Game Experience and it's downward spiral, had numerous worlds and people would create player cities and build their own homes and decorate them and so on, and people had professions like Dancer or Musician as well as Bounty Hunter and so on.
It may be that a "pure sandbox" kind of MMO won't work any more, as the MMO market has grown, but it'd be interesting to try and Fallout seems a world ripe for it (Fallen Earth was a fun MMO, for example, and set in a similar world).
Only thing that makes me really nervous about a Fallout MMO would be how to distinguish player A from player B. In Fallout, there's only so many ways to play... sneaky melee, sneaky sniper, chem-user (or not), minigun - power armor - hulk, etc... and really those amount to gear choices. If you consider SPECIAL and Perks to be the "class" defining attributes, then I suppose you could have a high CHA/INT "Smooth Talker" with Wasteland Whisperer perks and so on.... and have a high END/INT character with a lot of the Chem resistance / duration-boosting perks (a "Juicer", as they were called in the RIFTS pen-and-paper RPG back in the day).
But to reiterate, I think a more sandbox, less Global Messiah Grand Main Quest would be preferable.