I understand the mechanical differences between the two games (notably, approaches instead of skills and a consolidated stress track), but is FATE Accelerated Edition simply meant to be "FATE Core Lite"? That is, is FAE meant to let new players get started with the system quickly while expecting that they will graduate to FATE Core at some point?
If this is not the case, what are the key differences that I should be aware of in my decision-making process as I pick between the two systems for my games? My primary concern is one of whether the added complexity of Core over Accelerated is worth the increased depth that it provides, in terms of storytelling possibilities and narrative pace. With my group's busy schedules, we prefer quickly-resolved conflicts to drawn out brawls, while maintaining some mechanical depth and flexibility in our narratives.
Best Answer
I wouldn't call FAE a "lite" version of Fate because it is a complete game. There aren't any gaps in the ruleset where you have to graduate to the "full" version. FAE does let new players get started quickly, but you could also use FAE to transition a group of habitual Dungeons and Dragons players to Fate.
Differences
As RPG systems go, Fate Core is on the light side of what I would call "rules-medium". It has a robust skill list that follows the traditional RPG pattern (albeit simplified), which serves to differentiate characters by what they can do. The driving factor in assembling a character sheet is education, and advancement implies further training or practice in the field.
Since the skills list is the only really granular part of the central Fate system, simplifying it and abstracting it further makes it very much a rules-light system. The simplified skill list has been renamed and re-themed to express the character's personality. In FAE, what the character can accomplish doesn't matter as much as how the character accomplishes it. Harry Dresden can throw a punch, burn a building down, or intimidate a magical malcontent because all of those things tap into his Forceful personality.
Making the Choice
There are two questions that you should ask:
Do I want characters' skills or their personalities to be more important to how they approach conflicts?
How quickly do I want players to be able to create characters and get into the game?
Those answers should point one way or another.