I have bought Fate Accelerated (FAE). I think the idea is laudable and the booklet is very nice. I dislike the art, but that is just me. As I wrote before, many people might actually like FAE better than Core, on the account of its being more streamlined and “pure”. Still, I think that there is at least one objective problem that is bound to complicate things in play. Now, mind you: I am not roleplaying these days, let alone playing FAE, so obviously I have not experienced such problems personally. So, if you are one of those self-righteous forum animals who like to say “actual play examples, or I won’t listen”, stop reading now.
The problem lies in Approaches, which substitutes Skills in FAE. FAE Approaches do not represent what characters can do and how well they are at doing it (unlike Core‘s Skills), bur rather how good they are at doing anything in a certain style: Forceful, Sneaky, Flashy, etc. This abstracts away entirely from the competences of a character: a guy who is especially good at doing thing Forcefully is going to be able to put in practice this approach in all sorts of tasks, regardless of his training.
If you are a hardcore enemy of simulationism (whatever this is supposed to mean), I guess that the idea must be very appealing to you: “Screw GURPS! Who cares whether my mad scientist is a virologist or a geophysicist? She’s Clever!”. The problem is that since most actions can be described as performed in many different styles, players are able to frame any even marginally important action as performed with their strongest approach. There are going to be clear cases (you cannot “forcefully” befriend somebody, because that is intimidation and is a different action), but mostly, they will try and manage to do so. What you get, then, is first of all a game which is mechanically very monotonous: whenever it matters, you roll with your best value. Most importantly, it is also going to be a narratively cliched play in which the “brick” character always hits hard, the “sneaky” guy always sneaks around and so on. I hear you: worse things happen. Yeah, but still.
EDIT (10 June 2015): I have now in my hands a physical copy of FAE. The quality of the paper and the cover is very pleasant, like in everything by Evil Hat I have seen so far. But the choice of paperback binding (instead of staple binding) for meager 60 pages is ill advised: the booklet is guaranteed to fall apart after a few hours of game use. A pity.