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:

1. Do I want characters' skills or their personalities to be more important to how they approach conflicts?

2. 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.

Point by point comparison

Fate Core

• skill driven - characters competency is in specific fields of endeavor.
• Stress track increases from base with certain skills and certain stunts, thus not all are equally able to take stress
• Separate Physical and Mental stress tracks, plus optionally, Wealth, Magic, and Karma stress tracks.
• PC's by default start with one skill at Great (+4)
• 3 background related aspects. Plus up to 2 more of personal choice.
• Background created collaboratively
• 3-5 stunts

Fate Accelerated Edition

• approach driven - character competency is in how the task is approached, not in specific fields.
• Everyone has the same sized stress track and same number of consequence slots; everyone is thus equally able to take stress.
• one unified stress track.
• No PC starts better than good at anything.
• a high concept aspect, a trouble aspect, and 1-3 other aspects.
• No background required
• One stunt.

Implications

Fate Core

Fate core is somewhat grittier; characters are distinguished by skills and stunts as well as aspects, and can have widely different resistance to various kinds of stress. It's more "realistic" in that way. It's also more involved, and focuses on group collaboration.

Fate Accelerated

More cinematic. Characters differentiated primarily by their aspects and stunts, and are much more broadly competent, but less likely to be particularly skilled in any given area. Also, due to the ability to do character generation alone, the party need not generate together, so it's better for drop-in/drop-out campaigns and one-shots.