I have experience bringing kids (my own son and his friends) into RPGs. I have experience with Dungeon World. I have experience with Fate and FAE. However - I do not have experience introducing kids to RPGs with Dungeon World or FAE. Just to be explicitly clear.
With that being said, as the probable instigator of this question, I feel that it is incumbent upon me to at least attempt an answer, so here goes:
Both games are products of a new school of game design. They fall into a category I will call here Fiction First. In neither game is the answer to the question What do you do? present on the character sheet. Ever.
In a Fiction First game, the game is played by talking - it is a conversation, where the GM describes situations and then poses the essential question of roleplaying, What do you do? Players answer and the GM rolls the outcome of their answers back into the fiction and the cycle continues, permutes, and repeats.
Dungeon World is a very focused game, and it is focused upon the very genre you want to play. It is an excellent game in general, and has been an excellent vehicle for me to introduce new players - character creation is fun and collaborative and results in parties that are connected before the start of the adventure. When I warned before of the different principles, here is what I was warning you about:
Dungeon World is derived from the groundbreaking game Apocalypse World by D. Vincent Baker. One part of the brilliance of AW that shines through in DW is the concept of Moves. Moves encapsulate the mechanics of Dungeon World. You've seen them. Player moves read like this:
When you attack an enemy in melee, roll+Str. ✴On a 10+, you deal your damage to the enemy and avoid their attack. At your option, you may choose to do +1d6 damage but expose yourself to the enemy’s attack. ✴On a 7–9, you deal your damage to the enemy and the enemy makes an attack against you.
That's Hack and Slash, a basic player move, from the DW SRD.
The structure of a move is very important - it defines an inflection point in the fiction - a point at which the mechanics kick in - and describes simply but exactly what to do and how to fold the result back into the fiction. A move is invoked by an action in the fiction that triggers it. But a player may never state, "I Hack and Slash the ogre!" - The player has to describe something that triggers the move instead. This is what I mean about the answer not being on the character sheet. This is confusing to some people, especially those used to selecting options from video game menus or boardgame actions.
But Dungeon World is an asymmetrical game. You, the GM, are not playing the same game as the players are. The GM has moves, yes, but they are not the same as player moves. They do not have a trigger/roll/consequence structure. You, as the GM, will probably never roll dice. I usually have my players roll damage for my monsters and other threats. Your moves are things that just happen in the fiction. You say it, it happens. From the gazeteer:
Whenever everyone looks to you to see what happens choose one of these. Each move is something that occurs in the fiction of the game—they aren't code words or special terms. "Use up their resources" literally means to expend the resources of the characters, for example.
- Use a monster, danger, or location move
- Reveal an unwelcome truth
- Show signs of an approaching threat
- Deal damage
- Use up their resources
- Turn their move back on them
- Separate them
- Give an opportunity that fits a class’ abilities
- Show a downside to their class, race, or equipment
- Offer an opportunity, with or without cost
- Put someone in a spot
- Tell them the requirements or consequences and ask
So - players take fictional actions and trigger moves. You use your moves to create fictional actions and / or situations. If a monster has a move like Call for reinforcements, that's exactly what it is - but there will be no check, no percentage chance that reinforcements hear them - what happens is what makes sense in the story. Are all the other goblins (or whatever) dead? Did they already call for reinforcements? Did the players already eliminate or make a deal with those reinforcements? Are they too far from the lair to hear? That's all up to you and what makes sense given the story so far.
You don't really need much in the way of a planned adventure for Dungeon World, I have found. A juicy starting situation and a little local information, plus whatever you think would be super fun to throw at the players is usually plenty. The events tend to spin off on their own as players act and the rules are engaged.
Fate Core (and FAE, by extension) is a generic game - not generic in the bad sense of "low quality" or "one-size-fits none". Rather, FAE is generic in that it is designed to create adventurous stories through play, while the genre forms, tropes, settings, and specifics of those stories are outside the scope of the system.
The heart of Fate is Characters - though many mistake the (once-novel, now at least 8 years old) concept of Aspects for the game's core. Aspects are great, and they were once novel, and they changed the way I play everything. But you'll understand it better if you think of it as Characters - thus, the Fate Fractal. From the SRD:
In Fate, you can treat anything in the game world like it’s a character. Anything can have aspects, skills, stunts, stress tracks, and consequences if you need it to.
Aspects are just one piece of Characters, and a very flexible piece, but don't forget you have the whole palette of tools to choose from and get stuck using just aspects.
The brilliance of Fate Core (and therefore FAE, I'm going to stop mentioning it now) is the distillation of everything in the game down into just four actions:
- Create an Advantage
While Dungeon World provides specific moves that guide play out of the fiction, into the mechanics, and back, Fate sets general guidelines that do the same things. So one set of mechanics governs every interaction between the mechanics and the fiction, dispelling the need for the profusion of systems and subsystems that practically defined early RPGs.
So if your player says, "I want to take careful aim with my crossbow so I can be sure to hit the bad guy and not the hostage!" you take that as Creating an Advantage instead of consulting the book to find out if aiming is a free action, whether the player meets the minimum dexterity requirement, what the aim bonus for their particular crossbow is, etc. If they succeed in creating the advantage, you create the aspect You're in my sights! and proceed with play.
If you need something more complicated - the canonical example is On fire! - you can give it skills, like Burn for example, to take actions (like attacking or moving) with, and a stress track to show how far it is from being put out.
Fate isn't completely agnostic about what kind of stories it is designed to tell. What Fate seeks to model is adventure fiction - fun, exciting stories about interesting people doing risky things. And it does a great job of it.
- Neither game is hard to run or play.
- Neither is particularly expensive
- Both games are more similar to each other than to AD&D
- Both are wonderful games and I would not hesitate to use either one in the situation you describe
- If forced to choose, I would say Dungeon World - because in your instance, you have only a short time to play. If you had all summer, you might find that the broader scope of Fate allowed you to explore more genres.