I come to that question after getting the chance to GM some FateCore on Sunday with my at-home group (Wife+kids).
The basic setup is simple - the players are the crew of a small "Space Ranger Cruiser" in a "24th Century: Outer Space!" setting. (No FTL, but tons of space flight.) They found out that someone has started manufacturing killbots in the asteroid belt when one attacked their base on Ceres. They managed to get into the hidden asteroid base with very little opposition (I let them try out some different types of skills and a handful of simple combats), and are poised to enter "Sector 8", which presumably is where all the killbots are being built. (In other words, I went for a straight-up dungeon crawl. At least in the classic games, that's usually a safe bet, though perhaps it was a poor choice for FateCore....)
Now here's the thing. We've mostly been playing traditional games like Pathfinder, and they're having a little trouble with the idea that THEY get to decide the details of a scene or setting. They are more used to the GM (me) laying it all out for them to explore and reacting instead of acting. I've tried to encourage them with questions like, "What do you think, DO these robots have homing beacons?" but like me, they're having some trouble adapting. So rather than a collaborative effort to make an epic story, this is turning into a plain-old "GM tells us what's happening, we react" game. I do like those kinds of games, but FateCore seems like it would work best with everyone creating the story and the GM just running the bad guys and making judgements about difficulty levels.
Maybe the stumbling block is that they don't have a significant buy-in in the setting. When I asked them what sort of setting they wanted to play, they were noncommittal, though interested to try FateCore. We already have a Fantasy game, so I proposed this "Tom Corbett, Space Cadet" type pulp setting as something different. It wasn't until I suggested to my son that he could play a Telepath "Psi-Corp Ranger" that he became more than passively interested in the setting, and my daughter was only interested in playing an "Anime School Girl Brat" whose dad is a Space Ranger officer. Both turned out to be pretty cool characters in the end, but I'm afraid that having a dungeon crawl be their first outing might have been a mistake, since none of them really wants to help "own" the story.
I've also found that it's not easy to work their individual Aspects into the game. As I mentioned, this is more or less a straight-up dungeon crawl, though the characters are more tuned for investigative work. Which is my fault - I fell back on the "tried & true" without regard for how their characters turned out. To their credit, they are taking guard uniforms for disguise and the telepath is lifting names out of peoples' heads to help deceive them.
I know that attempting to GM a game I've never played for a group that's never played the game, and isn't super-invested in the setting is rife with failure possibilities. (When I put it that way, it seems insane that I even tried.) I'm not judging FateCore (which is a very slick rule set), just my ability to employ it properly with the players I have.
It hasn't all been bad - we had some pretty serious laughs when the guards caught the party in the Hydroponics sector, and the School Girl ("I'm really not as young as I look!") used her considerable deception skill to trick the guards into believing that she and one of the other characters were "just being naughty, and please, please, please don't let my dad find out!" She distracted the guards with her Legendary Deception long enough for the "hitter" to slug one in the Jaw (lights out!) and the third character secured the second guard with zip ties and duct tape. (Because even in C24, duct tape is the answer.)
It might be best to, after we finish this scenario, say, "Ok, that's how FateCore works, more or less. Now what sort of game do you REALLY want to play?"
And I have to be OK with it if they say, "Pathfinder!"