I love the Amber Diceless system. Had quite a bit of fun with it. If I had to explain Fate to someone who'd only played Amber and D&D I think I'd compare it more to Amber.
Your character's skills are a lot like Amber attributes broken down into more specific areas. D&D style attributes are basically not present in either of the other systems.
Aspects and Fate points are a lot like Stuff in Amber. Like skills, Aspects are broken down a bit more than their Amber equivalent. You have multiple Aspects and because the world setting for the Dresden Files is more about gray areas than Amber is, the best Aspects can be looked at in both a positive and a negative light, like the "barbarian" example above. So Aspects handle whether you have positive or negative Stuff, while Fate points are the actual measure of it. The usual style for gameplay is to complicate the life of the characters by drawing on or "compelling" Aspects in a negative way and both the GM and players can get involved in that (subject to GM approval of course). Then when the plot comes to a climax you have resources to burn.
One important note about Aspects is that they're all over. They're basicall soundbyte sized descriptions of what something is, what it's tied to, etc. In Amber you're encouraged to add details to your surroundings subject to GM approval. In the DFRPG you do the same thing by declaring an Aspect but there are rolls involved. This may feel a little complex at first but mostly as a player you should just keep in mind that you should just keep in mind that like in Amber you're a lot better off interacting and taking a role in the narrative of the story than just hiding behind numbers.
Powers are actually very similar to powers in Amber. Stunts are a bit like having a rank in an Amber attribute. You're good enough with one area of a skill that it requires special description.
The rest past that is details. You'll have to decide how much nuts and bolts you want them to handle and how much you're willing to smooth over in the first few games to get the ball rolling. Fate has some really wonderful ideas. To be honest, as much as I like Amber, if I ran it again I'd be incorporating some of the ideas I've seen in Fate and the DFRPG. But the downside of that is that they're new ideas. I don't think it's really possible at this point to start a new group in Fate without handling a lot of the mechanics for them. Must see if Fred has a World Conquest fund going or something.