Moving on from the issue of "how similar" to "in what ways similar/different":
I don't think Fate has the idea of using aspects to convey what's at stake in a scene. This is one thing I really like in MHRP/Cortex+ Heroic, and have used more as I've become more comfortable with the system. For @Micah Sweet, though, it might be a bit "metagamey", as it can require some negotiation with the players to settle what's at stake. Not always - Being Pursued by Giants might be a GM-imposed outcome of an earlier scene. But sometimes - Not Sure of What to Do Next couldn't be imposed as a Scene Distinction if the players were dead-set on their next goal!Scene Distinctions are roughly equivalent to Situation Aspects.
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Fate also includes Challenges, akin to 4e Skill Challenges.
But the Fate GM has unlimited fate points for compels, don't they? Whereas Limits have to be paid for by spending Doom Pool dice, unless the player chooses to take a Plot Point instead.Fate doesn't have a Doom Pool per se, but the GM does have a number of Fate points for running a scene, which may also involve conceding a scene: GM Fate Points.